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031-b-y-h-ng-ng-th-c-ng-nh-la-gi [2018/11/07 17:13] (current)
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 +<​HTML><​br><​div id="​mw-content-text"​ lang="​vi"​ dir="​ltr"><​div class="​mw-parser-output"><​p>​Trong toán học sơ cấp, <​b>​bảy hằng đẳng thức đáng nhớ</​b>​ là những đẳng thức cơ bản nhất mà mỗi người học toán cần phải nắm vững. Các đẳng thức được chứng minh bằng phép nhân đa thức với đa thức. Những đẳng thức này được sử dụng thường xuyên trong các bài toán liên quan đến giải phương trình, nhân chia các đa thức, biến đổi biểu thức tại cấp học trung học cơ sở và trung học phổ thông. Học thuộc bảy hằng đẳng thức đáng nhớ giúp giải nhanh những bài toán phân tích đa thức thành nhân tử.
 +</​p><​p>​Trong những hằng đẳng thức này, một bên dấu bằng là tổng hoặc hiệu và bên gọi lại là tích hoặc lũy thừa. Bảy hằng đẳng thức đáng nhớ được in trong sách giáo khoa bậc trung học cơ sở ở Việt Nam và được in rất nhiều trong bìa sau của vở viết cấp II hoặc cấp III của học sinh.
 +</p>
  
 +
 +<​h2><​span id="​C.C3.A1c_h.E1.BA.B1ng_.C4.91.E1.BA.B3ng_th.E1.BB.A9c"/><​span class="​mw-headline"​ id="​Các_hằng_đẳng_thức">​Các hằng đẳng thức</​span></​h2>​
 +<​ol><​li><​b>​Bình phương của một tổng:</​b>​
 +<​dl><​dd><​span class="​mwe-math-element"><​span class="​mwe-math-mathml-inline mwe-math-mathml-a11y"​ style="​display:​ none;"><​math xmlns="​http://​www.w3.org/​1998/​Math/​MathML"​ alttext="​{displaystyle (a+b)^{2}=a^{2}+2ab+b^{2},​}"><​semantics><​mrow class="​MJX-TeXAtom-ORD"><​mstyle displaystyle="​true"​ scriptlevel="​0"><​mo stretchy="​false">​(</​mo><​mi>​a</​mi><​mo>​+</​mo><​mi>​b</​mi><​msup><​mo stretchy="​false">​)</​mo><​mrow class="​MJX-TeXAtom-ORD"><​mn>​2</​mn></​mrow></​msup><​mo>​=</​mo><​msup><​mi>​a</​mi><​mrow class="​MJX-TeXAtom-ORD"><​mn>​2</​mn></​mrow></​msup><​mo>​+</​mo><​mn>​2</​mn><​mi>​a</​mi><​mi>​b</​mi><​mo>​+</​mo><​msup><​mi>​b</​mi><​mrow class="​MJX-TeXAtom-ORD"><​mn>​2</​mn></​mrow></​msup><​mspace width="​thinmathspace"/></​mstyle></​mrow><​annotation encoding="​application/​x-tex">​{displaystyle (a+b)^{2}=a^{2}+2ab+b^{2},​}</​annotation></​semantics></​math></​span><​img src="​https://​wikimedia.org/​api/​rest_v1/​media/​math/​render/​svg/​68a118ec24c36c8c70800e61f344aafdcbdb5d63"​ class="​mwe-math-fallback-image-inline"​ aria-hidden="​true"​ style="​vertical-align:​ -0.838ex; width:​24.823ex;​ height:​3.176ex;"​ alt="​{displaystyle (a+b)^{2}=a^{2}+2ab+b^{2},​}"/></​span></​dd></​dl></​li>​
 +<​li><​b>​Bình phương của một hiệu:</​b>​
 +<​dl><​dd><​span class="​mwe-math-element"><​span class="​mwe-math-mathml-inline mwe-math-mathml-a11y"​ style="​display:​ none;"><​math xmlns="​http://​www.w3.org/​1998/​Math/​MathML"​ alttext="​{displaystyle (a-b)^{2}=a^{2}-2ab+b^{2},​}"><​semantics><​mrow class="​MJX-TeXAtom-ORD"><​mstyle displaystyle="​true"​ scriptlevel="​0"><​mo stretchy="​false">​(</​mo><​mi>​a</​mi><​mo>​−<​!-- &minus; --></​mo><​mi>​b</​mi><​msup><​mo stretchy="​false">​)</​mo><​mrow class="​MJX-TeXAtom-ORD"><​mn>​2</​mn></​mrow></​msup><​mo>​=</​mo><​msup><​mi>​a</​mi><​mrow class="​MJX-TeXAtom-ORD"><​mn>​2</​mn></​mrow></​msup><​mo>​−<​!-- &minus; --></​mo><​mn>​2</​mn><​mi>​a</​mi><​mi>​b</​mi><​mo>​+</​mo><​msup><​mi>​b</​mi><​mrow class="​MJX-TeXAtom-ORD"><​mn>​2</​mn></​mrow></​msup><​mspace width="​thinmathspace"/></​mstyle></​mrow><​annotation encoding="​application/​x-tex">​{displaystyle (a-b)^{2}=a^{2}-2ab+b^{2},​}</​annotation></​semantics></​math></​span><​img src="​https://​wikimedia.org/​api/​rest_v1/​media/​math/​render/​svg/​2e45629c03fd6381b4fa315d9997d1dafb1b65ad"​ class="​mwe-math-fallback-image-inline"​ aria-hidden="​true"​ style="​vertical-align:​ -0.838ex; width:​24.823ex;​ height:​3.176ex;"​ alt="​{displaystyle (a-b)^{2}=a^{2}-2ab+b^{2},​}"/></​span></​dd></​dl></​li>​
 +<​li><​b>​Hiệu hai bình phương:</​b>​
 +<​dl><​dd><​span class="​mwe-math-element"><​span class="​mwe-math-mathml-inline mwe-math-mathml-a11y"​ style="​display:​ none;"><​math xmlns="​http://​www.w3.org/​1998/​Math/​MathML"​ alttext="​{displaystyle a^{2}-b^{2}=(a-b)(a+b),​}"><​semantics><​mrow class="​MJX-TeXAtom-ORD"><​mstyle displaystyle="​true"​ scriptlevel="​0"><​msup><​mi>​a</​mi><​mrow class="​MJX-TeXAtom-ORD"><​mn>​2</​mn></​mrow></​msup><​mo>​−<​!-- &minus; --></​mo><​msup><​mi>​b</​mi><​mrow class="​MJX-TeXAtom-ORD"><​mn>​2</​mn></​mrow></​msup><​mo>​=</​mo><​mo stretchy="​false">​(</​mo><​mi>​a</​mi><​mo>​−<​!-- &minus; --></​mo><​mi>​b</​mi><​mo stretchy="​false">​)</​mo><​mo stretchy="​false">​(</​mo><​mi>​a</​mi><​mo>​+</​mo><​mi>​b</​mi><​mo stretchy="​false">​)</​mo><​mspace width="​thinmathspace"/></​mstyle></​mrow><​annotation encoding="​application/​x-tex">​{displaystyle a^{2}-b^{2}=(a-b)(a+b),​}</​annotation></​semantics></​math></​span><​img src="​https://​wikimedia.org/​api/​rest_v1/​media/​math/​render/​svg/​44580a505f13ea520ebd20c4f25015b3863098fa"​ class="​mwe-math-fallback-image-inline"​ aria-hidden="​true"​ style="​vertical-align:​ -0.838ex; width:​24.416ex;​ height:​3.176ex;"​ alt="​{displaystyle a^{2}-b^{2}=(a-b)(a+b),​}"/></​span></​dd></​dl></​li>​
 +<​li><​b>​Lập phương của một tổng:</​b>​
 +<​dl><​dd><​span class="​mwe-math-element"><​span class="​mwe-math-mathml-inline mwe-math-mathml-a11y"​ style="​display:​ none;"><​math xmlns="​http://​www.w3.org/​1998/​Math/​MathML"​ alttext="​{displaystyle (a+b)^{3}=a^{3}+3a^{2}b+3ab^{2}+b^{3},​}"><​semantics><​mrow class="​MJX-TeXAtom-ORD"><​mstyle displaystyle="​true"​ scriptlevel="​0"><​mo stretchy="​false">​(</​mo><​mi>​a</​mi><​mo>​+</​mo><​mi>​b</​mi><​msup><​mo stretchy="​false">​)</​mo><​mrow class="​MJX-TeXAtom-ORD"><​mn>​3</​mn></​mrow></​msup><​mo>​=</​mo><​msup><​mi>​a</​mi><​mrow class="​MJX-TeXAtom-ORD"><​mn>​3</​mn></​mrow></​msup><​mo>​+</​mo><​mn>​3</​mn><​msup><​mi>​a</​mi><​mrow class="​MJX-TeXAtom-ORD"><​mn>​2</​mn></​mrow></​msup><​mi>​b</​mi><​mo>​+</​mo><​mn>​3</​mn><​mi>​a</​mi><​msup><​mi>​b</​mi><​mrow class="​MJX-TeXAtom-ORD"><​mn>​2</​mn></​mrow></​msup><​mo>​+</​mo><​msup><​mi>​b</​mi><​mrow class="​MJX-TeXAtom-ORD"><​mn>​3</​mn></​mrow></​msup><​mspace width="​thinmathspace"/></​mstyle></​mrow><​annotation encoding="​application/​x-tex">​{displaystyle (a+b)^{3}=a^{3}+3a^{2}b+3ab^{2}+b^{3},​}</​annotation></​semantics></​math></​span><​img src="​https://​wikimedia.org/​api/​rest_v1/​media/​math/​render/​svg/​09ad4763b3734239fded9c0ea6380c7e9fc3c24a"​ class="​mwe-math-fallback-image-inline"​ aria-hidden="​true"​ style="​vertical-align:​ -0.838ex; width:​33.162ex;​ height:​3.176ex;"​ alt="​{displaystyle (a+b)^{3}=a^{3}+3a^{2}b+3ab^{2}+b^{3},​}"/></​span></​dd></​dl></​li>​
 +<​li><​b>​Lập phương của một hiệu:</​b>​
 +<​dl><​dd><​span class="​mwe-math-element"><​span class="​mwe-math-mathml-inline mwe-math-mathml-a11y"​ style="​display:​ none;"><​math xmlns="​http://​www.w3.org/​1998/​Math/​MathML"​ alttext="​{displaystyle (a-b)^{3}=a^{3}-3a^{2}b+3ab^{2}-b^{3},​}"><​semantics><​mrow class="​MJX-TeXAtom-ORD"><​mstyle displaystyle="​true"​ scriptlevel="​0"><​mo stretchy="​false">​(</​mo><​mi>​a</​mi><​mo>​−<​!-- &minus; --></​mo><​mi>​b</​mi><​msup><​mo stretchy="​false">​)</​mo><​mrow class="​MJX-TeXAtom-ORD"><​mn>​3</​mn></​mrow></​msup><​mo>​=</​mo><​msup><​mi>​a</​mi><​mrow class="​MJX-TeXAtom-ORD"><​mn>​3</​mn></​mrow></​msup><​mo>​−<​!-- &minus; --></​mo><​mn>​3</​mn><​msup><​mi>​a</​mi><​mrow class="​MJX-TeXAtom-ORD"><​mn>​2</​mn></​mrow></​msup><​mi>​b</​mi><​mo>​+</​mo><​mn>​3</​mn><​mi>​a</​mi><​msup><​mi>​b</​mi><​mrow class="​MJX-TeXAtom-ORD"><​mn>​2</​mn></​mrow></​msup><​mo>​−<​!-- &minus; --></​mo><​msup><​mi>​b</​mi><​mrow class="​MJX-TeXAtom-ORD"><​mn>​3</​mn></​mrow></​msup><​mspace width="​thinmathspace"/></​mstyle></​mrow><​annotation encoding="​application/​x-tex">​{displaystyle (a-b)^{3}=a^{3}-3a^{2}b+3ab^{2}-b^{3},​}</​annotation></​semantics></​math></​span><​img src="​https://​wikimedia.org/​api/​rest_v1/​media/​math/​render/​svg/​970bd2f5fb8335243e0d780b4d5a63e15a8e74f7"​ class="​mwe-math-fallback-image-inline"​ aria-hidden="​true"​ style="​vertical-align:​ -0.838ex; width:​33.162ex;​ height:​3.176ex;"​ alt="​{displaystyle (a-b)^{3}=a^{3}-3a^{2}b+3ab^{2}-b^{3},​}"/></​span></​dd></​dl></​li>​
 +<​li><​b>​Tổng hai lập phương:</​b>​
 +<​dl><​dd><​span class="​mwe-math-element"><​span class="​mwe-math-mathml-inline mwe-math-mathml-a11y"​ style="​display:​ none;"><​math xmlns="​http://​www.w3.org/​1998/​Math/​MathML"​ alttext="​{displaystyle a^{3}+b^{3}=(a+b)(a^{2}-ab+b^{2})=(a+b)^{3}-3a^{2}b-3ab^{2}=(a+b)^{3}-3ab(a+b)}"><​semantics><​mrow class="​MJX-TeXAtom-ORD"><​mstyle displaystyle="​true"​ scriptlevel="​0"><​msup><​mi>​a</​mi><​mrow class="​MJX-TeXAtom-ORD"><​mn>​3</​mn></​mrow></​msup><​mo>​+</​mo><​msup><​mi>​b</​mi><​mrow class="​MJX-TeXAtom-ORD"><​mn>​3</​mn></​mrow></​msup><​mo>​=</​mo><​mo stretchy="​false">​(</​mo><​mi>​a</​mi><​mo>​+</​mo><​mi>​b</​mi><​mo stretchy="​false">​)</​mo><​mo stretchy="​false">​(</​mo><​msup><​mi>​a</​mi><​mrow class="​MJX-TeXAtom-ORD"><​mn>​2</​mn></​mrow></​msup><​mo>​−<​!-- &minus; --></​mo><​mi>​a</​mi><​mi>​b</​mi><​mo>​+</​mo><​msup><​mi>​b</​mi><​mrow class="​MJX-TeXAtom-ORD"><​mn>​2</​mn></​mrow></​msup><​mo stretchy="​false">​)</​mo><​mo>​=</​mo><​mo stretchy="​false">​(</​mo><​mi>​a</​mi><​mo>​+</​mo><​mi>​b</​mi><​msup><​mo stretchy="​false">​)</​mo><​mrow class="​MJX-TeXAtom-ORD"><​mn>​3</​mn></​mrow></​msup><​mo>​−<​!-- &minus; --></​mo><​mn>​3</​mn><​msup><​mi>​a</​mi><​mrow class="​MJX-TeXAtom-ORD"><​mn>​2</​mn></​mrow></​msup><​mi>​b</​mi><​mo>​−<​!-- &minus; --></​mo><​mn>​3</​mn><​mi>​a</​mi><​msup><​mi>​b</​mi><​mrow class="​MJX-TeXAtom-ORD"><​mn>​2</​mn></​mrow></​msup><​mo>​=</​mo><​mo stretchy="​false">​(</​mo><​mi>​a</​mi><​mo>​+</​mo><​mi>​b</​mi><​msup><​mo stretchy="​false">​)</​mo><​mrow class="​MJX-TeXAtom-ORD"><​mn>​3</​mn></​mrow></​msup><​mo>​−<​!-- &minus; --></​mo><​mn>​3</​mn><​mi>​a</​mi><​mi>​b</​mi><​mo stretchy="​false">​(</​mo><​mi>​a</​mi><​mo>​+</​mo><​mi>​b</​mi><​mo stretchy="​false">​)</​mo></​mstyle></​mrow><​annotation encoding="​application/​x-tex">​{displaystyle a^{3}+b^{3}=(a+b)(a^{2}-ab+b^{2})=(a+b)^{3}-3a^{2}b-3ab^{2}=(a+b)^{3}-3ab(a+b)}</​annotation></​semantics></​math></​span><​img src="​https://​wikimedia.org/​api/​rest_v1/​media/​math/​render/​svg/​2ff56e6f6511306ae06303a6d9ae18191ac21cae"​ class="​mwe-math-fallback-image-inline"​ aria-hidden="​true"​ style="​vertical-align:​ -0.838ex; width:​80.941ex;​ height:​3.176ex;"​ alt="​{displaystyle a^{3}+b^{3}=(a+b)(a^{2}-ab+b^{2})=(a+b)^{3}-3a^{2}b-3ab^{2}=(a+b)^{3}-3ab(a+b)}"/></​span></​dd></​dl></​li>​
 +<​li><​b>​Hiệu hai lập phương:</​b>​
 +<​dl><​dd><​span class="​mwe-math-element"><​span class="​mwe-math-mathml-inline mwe-math-mathml-a11y"​ style="​display:​ none;"><​math xmlns="​http://​www.w3.org/​1998/​Math/​MathML"​ alttext="​{displaystyle a^{3}-b^{3}=(a-b)(a^{2}+ab+b^{2})=(a-b)^{3}+3a^{2}b-3ab^{2}=(a-b)^{3}+3ab(a-b)}"><​semantics><​mrow class="​MJX-TeXAtom-ORD"><​mstyle displaystyle="​true"​ scriptlevel="​0"><​msup><​mi>​a</​mi><​mrow class="​MJX-TeXAtom-ORD"><​mn>​3</​mn></​mrow></​msup><​mo>​−<​!-- &minus; --></​mo><​msup><​mi>​b</​mi><​mrow class="​MJX-TeXAtom-ORD"><​mn>​3</​mn></​mrow></​msup><​mo>​=</​mo><​mo stretchy="​false">​(</​mo><​mi>​a</​mi><​mo>​−<​!-- &minus; --></​mo><​mi>​b</​mi><​mo stretchy="​false">​)</​mo><​mo stretchy="​false">​(</​mo><​msup><​mi>​a</​mi><​mrow class="​MJX-TeXAtom-ORD"><​mn>​2</​mn></​mrow></​msup><​mo>​+</​mo><​mi>​a</​mi><​mi>​b</​mi><​mo>​+</​mo><​msup><​mi>​b</​mi><​mrow class="​MJX-TeXAtom-ORD"><​mn>​2</​mn></​mrow></​msup><​mo stretchy="​false">​)</​mo><​mo>​=</​mo><​mo stretchy="​false">​(</​mo><​mi>​a</​mi><​mo>​−<​!-- &minus; --></​mo><​mi>​b</​mi><​msup><​mo stretchy="​false">​)</​mo><​mrow class="​MJX-TeXAtom-ORD"><​mn>​3</​mn></​mrow></​msup><​mo>​+</​mo><​mn>​3</​mn><​msup><​mi>​a</​mi><​mrow class="​MJX-TeXAtom-ORD"><​mn>​2</​mn></​mrow></​msup><​mi>​b</​mi><​mo>​−<​!-- &minus; --></​mo><​mn>​3</​mn><​mi>​a</​mi><​msup><​mi>​b</​mi><​mrow class="​MJX-TeXAtom-ORD"><​mn>​2</​mn></​mrow></​msup><​mo>​=</​mo><​mo stretchy="​false">​(</​mo><​mi>​a</​mi><​mo>​−<​!-- &minus; --></​mo><​mi>​b</​mi><​msup><​mo stretchy="​false">​)</​mo><​mrow class="​MJX-TeXAtom-ORD"><​mn>​3</​mn></​mrow></​msup><​mo>​+</​mo><​mn>​3</​mn><​mi>​a</​mi><​mi>​b</​mi><​mo stretchy="​false">​(</​mo><​mi>​a</​mi><​mo>​−<​!-- &minus; --></​mo><​mi>​b</​mi><​mo stretchy="​false">​)</​mo></​mstyle></​mrow><​annotation encoding="​application/​x-tex">​{displaystyle a^{3}-b^{3}=(a-b)(a^{2}+ab+b^{2})=(a-b)^{3}+3a^{2}b-3ab^{2}=(a-b)^{3}+3ab(a-b)}</​annotation></​semantics></​math></​span><​img src="​https://​wikimedia.org/​api/​rest_v1/​media/​math/​render/​svg/​32c354b7cfc86cc809b94121963deb21440d7ceb"​ class="​mwe-math-fallback-image-inline"​ aria-hidden="​true"​ style="​vertical-align:​ -0.838ex; width:​80.941ex;​ height:​3.176ex;"​ alt="​{displaystyle a^{3}-b^{3}=(a-b)(a^{2}+ab+b^{2})=(a-b)^{3}+3a^{2}b-3ab^{2}=(a-b)^{3}+3ab(a-b)}"/></​span></​dd></​dl></​li></​ol><​h2><​span id="​C.C3.A1c_h.E1.BB.87_th.E1.BB.A9c_li.C3.AAn_quan"/><​span class="​mw-headline"​ id="​Các_hệ_thức_liên_quan">​Các hệ thức liên quan</​span></​h2>​
 +<​ol><​li><​span class="​mwe-math-element"><​span class="​mwe-math-mathml-inline mwe-math-mathml-a11y"​ style="​display:​ none;"><​math xmlns="​http://​www.w3.org/​1998/​Math/​MathML"​ alttext="​{displaystyle (a+b+c)^{3}=a^{3}+b^{3}+c^{3}+3(a+b)(b+c)(c+a),​}"><​semantics><​mrow class="​MJX-TeXAtom-ORD"><​mstyle displaystyle="​true"​ scriptlevel="​0"><​mo stretchy="​false">​(</​mo><​mi>​a</​mi><​mo>​+</​mo><​mi>​b</​mi><​mo>​+</​mo><​mi>​c</​mi><​msup><​mo stretchy="​false">​)</​mo><​mrow class="​MJX-TeXAtom-ORD"><​mn>​3</​mn></​mrow></​msup><​mo>​=</​mo><​msup><​mi>​a</​mi><​mrow class="​MJX-TeXAtom-ORD"><​mn>​3</​mn></​mrow></​msup><​mo>​+</​mo><​msup><​mi>​b</​mi><​mrow class="​MJX-TeXAtom-ORD"><​mn>​3</​mn></​mrow></​msup><​mo>​+</​mo><​msup><​mi>​c</​mi><​mrow class="​MJX-TeXAtom-ORD"><​mn>​3</​mn></​mrow></​msup><​mo>​+</​mo><​mn>​3</​mn><​mo stretchy="​false">​(</​mo><​mi>​a</​mi><​mo>​+</​mo><​mi>​b</​mi><​mo stretchy="​false">​)</​mo><​mo stretchy="​false">​(</​mo><​mi>​b</​mi><​mo>​+</​mo><​mi>​c</​mi><​mo stretchy="​false">​)</​mo><​mo stretchy="​false">​(</​mo><​mi>​c</​mi><​mo>​+</​mo><​mi>​a</​mi><​mo stretchy="​false">​)</​mo><​mspace width="​thinmathspace"/></​mstyle></​mrow><​annotation encoding="​application/​x-tex">​{displaystyle (a+b+c)^{3}=a^{3}+b^{3}+c^{3}+3(a+b)(b+c)(c+a),​}</​annotation></​semantics></​math></​span><​img src="​https://​wikimedia.org/​api/​rest_v1/​media/​math/​render/​svg/​33f464f6b0f64e8e77ed75a203de41dba9f09dd0"​ class="​mwe-math-fallback-image-inline"​ aria-hidden="​true"​ style="​vertical-align:​ -0.838ex; width:​51.762ex;​ height:​3.176ex;"​ alt="​{displaystyle (a+b+c)^{3}=a^{3}+b^{3}+c^{3}+3(a+b)(b+c)(c+a),​}"/></​span></​li>​
 +<​li><​span class="​mwe-math-element"><​span class="​mwe-math-mathml-inline mwe-math-mathml-a11y"​ style="​display:​ none;"><​math xmlns="​http://​www.w3.org/​1998/​Math/​MathML"​ alttext="​{displaystyle a^{3}+b^{3}+c^{3}-3abc=(a+b+c)(a^{2}+b^{2}+c^{2}-ab-bc-ca),​}"><​semantics><​mrow class="​MJX-TeXAtom-ORD"><​mstyle displaystyle="​true"​ scriptlevel="​0"><​msup><​mi>​a</​mi><​mrow class="​MJX-TeXAtom-ORD"><​mn>​3</​mn></​mrow></​msup><​mo>​+</​mo><​msup><​mi>​b</​mi><​mrow class="​MJX-TeXAtom-ORD"><​mn>​3</​mn></​mrow></​msup><​mo>​+</​mo><​msup><​mi>​c</​mi><​mrow class="​MJX-TeXAtom-ORD"><​mn>​3</​mn></​mrow></​msup><​mo>​−<​!-- &minus; --></​mo><​mn>​3</​mn><​mi>​a</​mi><​mi>​b</​mi><​mi>​c</​mi><​mo>​=</​mo><​mo stretchy="​false">​(</​mo><​mi>​a</​mi><​mo>​+</​mo><​mi>​b</​mi><​mo>​+</​mo><​mi>​c</​mi><​mo stretchy="​false">​)</​mo><​mo stretchy="​false">​(</​mo><​msup><​mi>​a</​mi><​mrow class="​MJX-TeXAtom-ORD"><​mn>​2</​mn></​mrow></​msup><​mo>​+</​mo><​msup><​mi>​b</​mi><​mrow class="​MJX-TeXAtom-ORD"><​mn>​2</​mn></​mrow></​msup><​mo>​+</​mo><​msup><​mi>​c</​mi><​mrow class="​MJX-TeXAtom-ORD"><​mn>​2</​mn></​mrow></​msup><​mo>​−<​!-- &minus; --></​mo><​mi>​a</​mi><​mi>​b</​mi><​mo>​−<​!-- &minus; --></​mo><​mi>​b</​mi><​mi>​c</​mi><​mo>​−<​!-- &minus; --></​mo><​mi>​c</​mi><​mi>​a</​mi><​mo stretchy="​false">​)</​mo><​mspace width="​thinmathspace"/></​mstyle></​mrow><​annotation encoding="​application/​x-tex">​{displaystyle a^{3}+b^{3}+c^{3}-3abc=(a+b+c)(a^{2}+b^{2}+c^{2}-ab-bc-ca),​}</​annotation></​semantics></​math></​span><​img src="​https://​wikimedia.org/​api/​rest_v1/​media/​math/​render/​svg/​e564af51ddd5c06116f8abf000d28a62ee8c86c5"​ class="​mwe-math-fallback-image-inline"​ aria-hidden="​true"​ style="​vertical-align:​ -0.838ex; width:​62.401ex;​ height:​3.176ex;"​ alt="​{displaystyle a^{3}+b^{3}+c^{3}-3abc=(a+b+c)(a^{2}+b^{2}+c^{2}-ab-bc-ca),​}"/></​span></​li>​
 +<​li><​span class="​mwe-math-element"><​span class="​mwe-math-mathml-inline mwe-math-mathml-a11y"​ style="​display:​ none;"><​math xmlns="​http://​www.w3.org/​1998/​Math/​MathML"​ alttext="​{displaystyle (a-b-c)^{2}=a^{2}+b^{2}+c^{2}-2ab+2bc-2ca,​}"><​semantics><​mrow class="​MJX-TeXAtom-ORD"><​mstyle displaystyle="​true"​ scriptlevel="​0"><​mo stretchy="​false">​(</​mo><​mi>​a</​mi><​mo>​−<​!-- &minus; --></​mo><​mi>​b</​mi><​mo>​−<​!-- &minus; --></​mo><​mi>​c</​mi><​msup><​mo stretchy="​false">​)</​mo><​mrow class="​MJX-TeXAtom-ORD"><​mn>​2</​mn></​mrow></​msup><​mo>​=</​mo><​msup><​mi>​a</​mi><​mrow class="​MJX-TeXAtom-ORD"><​mn>​2</​mn></​mrow></​msup><​mo>​+</​mo><​msup><​mi>​b</​mi><​mrow class="​MJX-TeXAtom-ORD"><​mn>​2</​mn></​mrow></​msup><​mo>​+</​mo><​msup><​mi>​c</​mi><​mrow class="​MJX-TeXAtom-ORD"><​mn>​2</​mn></​mrow></​msup><​mo>​−<​!-- &minus; --></​mo><​mn>​2</​mn><​mi>​a</​mi><​mi>​b</​mi><​mo>​+</​mo><​mn>​2</​mn><​mi>​b</​mi><​mi>​c</​mi><​mo>​−<​!-- &minus; --></​mo><​mn>​2</​mn><​mi>​c</​mi><​mi>​a</​mi><​mspace width="​thinmathspace"/></​mstyle></​mrow><​annotation encoding="​application/​x-tex">​{displaystyle (a-b-c)^{2}=a^{2}+b^{2}+c^{2}-2ab+2bc-2ca,​}</​annotation></​semantics></​math></​span><​img src="​https://​wikimedia.org/​api/​rest_v1/​media/​math/​render/​svg/​3ea19befb78bda04ce5f84da581340c49fc3328c"​ class="​mwe-math-fallback-image-inline"​ aria-hidden="​true"​ style="​vertical-align:​ -0.838ex; width:​45.819ex;​ height:​3.176ex;"​ alt="​{displaystyle (a-b-c)^{2}=a^{2}+b^{2}+c^{2}-2ab+2bc-2ca,​}"/></​span></​li>​
 +<​li><​span class="​mwe-math-element"><​span class="​mwe-math-mathml-inline mwe-math-mathml-a11y"​ style="​display:​ none;"><​math xmlns="​http://​www.w3.org/​1998/​Math/​MathML"​ alttext="​{displaystyle (a+b+c)^{2}=a^{2}+b^{2}+c^{2}+2ab+2bc+2ca,​}"><​semantics><​mrow class="​MJX-TeXAtom-ORD"><​mstyle displaystyle="​true"​ scriptlevel="​0"><​mo stretchy="​false">​(</​mo><​mi>​a</​mi><​mo>​+</​mo><​mi>​b</​mi><​mo>​+</​mo><​mi>​c</​mi><​msup><​mo stretchy="​false">​)</​mo><​mrow class="​MJX-TeXAtom-ORD"><​mn>​2</​mn></​mrow></​msup><​mo>​=</​mo><​msup><​mi>​a</​mi><​mrow class="​MJX-TeXAtom-ORD"><​mn>​2</​mn></​mrow></​msup><​mo>​+</​mo><​msup><​mi>​b</​mi><​mrow class="​MJX-TeXAtom-ORD"><​mn>​2</​mn></​mrow></​msup><​mo>​+</​mo><​msup><​mi>​c</​mi><​mrow class="​MJX-TeXAtom-ORD"><​mn>​2</​mn></​mrow></​msup><​mo>​+</​mo><​mn>​2</​mn><​mi>​a</​mi><​mi>​b</​mi><​mo>​+</​mo><​mn>​2</​mn><​mi>​b</​mi><​mi>​c</​mi><​mo>​+</​mo><​mn>​2</​mn><​mi>​c</​mi><​mi>​a</​mi><​mspace width="​thinmathspace"/></​mstyle></​mrow><​annotation encoding="​application/​x-tex">​{displaystyle (a+b+c)^{2}=a^{2}+b^{2}+c^{2}+2ab+2bc+2ca,​}</​annotation></​semantics></​math></​span><​img src="​https://​wikimedia.org/​api/​rest_v1/​media/​math/​render/​svg/​35c2c1d4836e4688988933ea54d54662df829749"​ class="​mwe-math-fallback-image-inline"​ aria-hidden="​true"​ style="​vertical-align:​ -0.838ex; width:​45.819ex;​ height:​3.176ex;"​ alt="​{displaystyle (a+b+c)^{2}=a^{2}+b^{2}+c^{2}+2ab+2bc+2ca,​}"/></​span></​li>​
 +<​li><​span class="​mwe-math-element"><​span class="​mwe-math-mathml-inline mwe-math-mathml-a11y"​ style="​display:​ none;"><​math xmlns="​http://​www.w3.org/​1998/​Math/​MathML"​ alttext="​{displaystyle (a+b-c)^{2}=a^{2}+b^{2}+c^{2}+2ab-2bc-2ca,​}"><​semantics><​mrow class="​MJX-TeXAtom-ORD"><​mstyle displaystyle="​true"​ scriptlevel="​0"><​mo stretchy="​false">​(</​mo><​mi>​a</​mi><​mo>​+</​mo><​mi>​b</​mi><​mo>​−<​!-- &minus; --></​mo><​mi>​c</​mi><​msup><​mo stretchy="​false">​)</​mo><​mrow class="​MJX-TeXAtom-ORD"><​mn>​2</​mn></​mrow></​msup><​mo>​=</​mo><​msup><​mi>​a</​mi><​mrow class="​MJX-TeXAtom-ORD"><​mn>​2</​mn></​mrow></​msup><​mo>​+</​mo><​msup><​mi>​b</​mi><​mrow class="​MJX-TeXAtom-ORD"><​mn>​2</​mn></​mrow></​msup><​mo>​+</​mo><​msup><​mi>​c</​mi><​mrow class="​MJX-TeXAtom-ORD"><​mn>​2</​mn></​mrow></​msup><​mo>​+</​mo><​mn>​2</​mn><​mi>​a</​mi><​mi>​b</​mi><​mo>​−<​!-- &minus; --></​mo><​mn>​2</​mn><​mi>​b</​mi><​mi>​c</​mi><​mo>​−<​!-- &minus; --></​mo><​mn>​2</​mn><​mi>​c</​mi><​mi>​a</​mi><​mspace width="​thinmathspace"/></​mstyle></​mrow><​annotation encoding="​application/​x-tex">​{displaystyle (a+b-c)^{2}=a^{2}+b^{2}+c^{2}+2ab-2bc-2ca,​}</​annotation></​semantics></​math></​span><​img src="​https://​wikimedia.org/​api/​rest_v1/​media/​math/​render/​svg/​51768134f6b6b69ceae60b05c3243754390bcb1d"​ class="​mwe-math-fallback-image-inline"​ aria-hidden="​true"​ style="​vertical-align:​ -0.838ex; width:​45.819ex;​ height:​3.176ex;"​ alt="​{displaystyle (a+b-c)^{2}=a^{2}+b^{2}+c^{2}+2ab-2bc-2ca,​}"/></​span></​li></​ol><​h2><​span id="​Xem_th.C3.AAm"/><​span class="​mw-headline"​ id="​Xem_thêm">​Xem thêm</​span></​h2>​
 +<​h2><​span id="​Tham_kh.E1.BA.A3o"/><​span class="​mw-headline"​ id="​Tham_khảo">​Tham khảo</​span></​h2>​
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031-b-y-h-ng-ng-th-c-ng-nh-la-gi.txt · Last modified: 2018/11/07 17:13 (external edit)