Упр.18.12 ГДЗ Мерзляк Поляков 7 класс (Алгебра)

1) (3m-2n)^2+5m(4n-m); 2) (9x+2y)^2-(8x+3y)(4x-4y).

1. $$\begin{aligned} (3m-2n)^2+5m(4n-m) &= 9m^2-12mn+4n^2+20mn-5m^2 \\ &= 4m^2+8mn+4n^2 \\ &= (2m+2n)^2. \end{aligned}$$
2. $$\begin{aligned} (9x+2y)^2-(8x+3y)(4x-4y) &= 81x^2+36xy+4y^2-(32x^2-32xy+12xy-12y^2) \\ &= 81x^2+36xy+4y^2-32x^2+20xy+12y^2 \\ &= 49x^2+56xy+16y^2 \\ &= (7x+4y)^2. \end{aligned}$$

Ответ

1) $$(2m+2n)^2$$

2) $$(7x+4y)^2$$