Упр.396 ГДЗ Муравин 7 класс (Алгебра)

1) (а + b)^3; 2) (а — b)^3; 3)(а + b)^4; 4) (а — b)^4.

1) $$\begin{aligned}(a+b)^3&=(a+b)^2(a+b)\\&=(a^2+2ab+b^2)(a+b)\\&=a^3+a^2b+2a^2b+2ab^2+ab^2+b^3\\&=a^3+3a^2b+3ab^2+b^3.\end{aligned}$$

2) $$\begin{aligned}(a-b)^3&=(a-b)^2(a-b)\\&=(a^2-2ab+b^2)(a-b)\\&=a^3-a^2b-2a^2b+2ab^2+ab^2-b^3\\&=a^3-3a^2b+3ab^2-b^3.\end{aligned}$$

3) $$\begin{aligned}(a+b)^4&=(a+b)^2(a+b)^2\\&=(a^2+2ab+b^2)(a^2+2ab+b^2)\\&=a^4+2a^3b+a^2b^2+2a^3b+4a^2b^2+2ab^3+a^2b^2+2ab^3+b^4\\&=a^4+4a^3b+6a^2b^2+4ab^3+b^4.\end{aligned}$$

4) $$\begin{aligned}(a-b)^4&=(a-b)^2(a-b)^2\\&=(a^2-2ab+b^2)(a^2-2ab+b^2)\\&=a^4-2a^3b+a^2b^2-2a^3b+4a^2b^2-2ab^3+a^2b^2-2ab^3+b^4\\&=a^4-4a^3b+6a^2b^2-4ab^3+b^4.\end{aligned}$$

Ответ

1) $$a^3+3a^2b+3ab^2+b^3$$; 2) $$a^3-3a^2b+3ab^2-b^3$$; 3) $$a^4+4a^3b+6a^2b^2+4ab^3+b^4$$; 4) $$a^4-4a^3b+6a^2b^2-4ab^3+b^4$$.