Упр.21.26 ГДЗ Мерзляк Поляков 7 класс (Алгебра)

1) (5x-y^2 )(5x+y^2 )-2(15x-7y^2 )-40;
2) (3m-2n)(12m+5n)+3m(3n+4)-2(3n^2-20n+12).

1) Преобразуем выражение:

$$ (5x-y^2)(5x+y^2)-2(15x-7y^2)-40 $$
$$ =25x^2-y^4-30x+14y^2-40 $$
$$ =25x^2-30x+9-y^4+14y^2-49 $$
$$ =(25x^2-30x+9)-(y^4-14y^2+49) $$
$$ =(5x-3)^2-(y^2-7)^2 $$
$$ =(5x-3-y^2+7)(5x-3+y^2-7) $$
$$ =(5x-y^2+4)(5x+y^2-10). $$

2) Аналогично:

$$ (3m-2n)(12m+5n)+3m(3n+4)-2(3n^2-20n+12) $$
$$ =36m^2+15mn-24mn-10n^2+9mn+12m-6n^2+40n-24 $$
$$ =36m^2-16n^2+12m+40n-24 $$
$$ =36m^2+12m+1-(16n^2-40n+25) $$
$$ =(6m+1)^2-(4n-5)^2 $$
$$ =(6m+1-4n+5)(6m+1+4n-5) $$
$$ =(6m-4n+6)(6m+4n-4) $$
$$ =2(3m-2n+3)\cdot 2(3m+2n-2) $$
$$ =4(3m-2n+3)(3m+2n-2). $$

Ответ

1) $$(5x-y^2+4)(5x+y^2-10)$$

2) $$4(3m-2n+3)(3m+2n-2)$$