Question

помогите разложить на множники​

Answer 1

Ответ:

$- 4ab(a + b)(a - b);$

$2a{(a - b)^2}{(a + b)^2}({a^2} + 3{b^2});$

$4a(b + 1)$

Объяснение:

$(a + b){(a - b)^3} - (a - b){(a + b)^3} = (a + b)(a - b)\left( {{{(a - b)}^2} - {{(a + b)}^2}} \right) = \\=(a + b)(a - b)({a^2} - 2ab + {b^2} - {a^2} - 2ab - {b^2}) = - 4ab(a + b)(a - b);$

${(a - b)^2}{(a + b)^5} + {(a + b)^2}{(a - b)^5} = {(a - b)^2}{(a + b)^2}\left( {{{(a + b)}^3} + {{(a - b)}^3}} \right) = \\={(a - b)^2}{(a + b)^2}({a^3} + 3{a^2}b + 3a{b^2} + {b^3} + {a^3} - 3{a^2}b + 3a{b^2} - {b^3}) = \\={(a - b)^2}{(a + b)^2}(2{a^3} + 6a{b^2}) = 2a{(a - b)^2}{(a + b)^2}({a^2} + 3{b^2});$

$(a + b)(a + b + 2) - (a - b)(a - b - 2) = {(a + b)^2} + 2(a + b) - {(a - b)^2} + 2(a - b) = \\={(a + b)^2} - {(a - b)^2} + 2(a + b + a - b) = (a + b + a - b)(a + b - a + b) + 4a = \\=2a \cdot 2b + 4a = 4a(b + 1).$