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Akishevskaya
@Akishevskaya
December 2021
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Разложите на множители
(a+b)^3-(a-b)^3;
(a+b)^4-(a-b)^4
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mmb1
Verified answer
(a+b)^3-(a-b)^3=(a+b-a+b)((a+b)^2+(a-b)(a+b)+(a-b)^2)=2b(a^2+2ab+b^2+a^2-b^2+a^2-2ab+b^2)=2b(3a^2+b^2)
(a+b)^4-(a-b)^4=((a+b)^2-(a-b)^2)((a-b)^2+(a+b)^2)=(a^2+2ab+b^2-a^2+2ab-b^2)(a^2-2ab+b^2+a^2+2ab+b^2)=8ab(a^2+b^2)
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Answers & Comments
Verified answer
(a+b)^3-(a-b)^3=(a+b-a+b)((a+b)^2+(a-b)(a+b)+(a-b)^2)=2b(a^2+2ab+b^2+a^2-b^2+a^2-2ab+b^2)=2b(3a^2+b^2)(a+b)^4-(a-b)^4=((a+b)^2-(a-b)^2)((a-b)^2+(a+b)^2)=(a^2+2ab+b^2-a^2+2ab-b^2)(a^2-2ab+b^2+a^2+2ab+b^2)=8ab(a^2+b^2)