Упр.21.14 ГДЗ Мерзляк Поляков 7 класс (Алгебра)

1) (m^2-2m)^2-1; 4) 64x^2+48xy+9y^2-144;
2) 16-(m^2+4m)^2; 5) c^2-a^2+22a-121;
3) x^2-18xy+81y^2-z^2; 6) 100-25y^2-60x^2 y-36x^4.

1. $$\begin{aligned} (m^2-2m)^2-1&=(m^2-2m-1)(m^2-2m+1)\\ &=(m^2-2m-1)(m-1)^2. \end{aligned}$$
2. $$\begin{aligned} 16-(m^2+4m)^2&=(4-m^2-4m)(4+m^2+4m)\\ &=(4-4m-m^2)(m+2)^2. \end{aligned}$$
3. $$\begin{aligned} x^2-18xy+81y^2-z^2&=(x-9y)^2-z^2\\ &=(x-9y-z)(x-9y+z). \end{aligned}$$
4. $$\begin{aligned} 64x^2+48xy+9y^2-144&=(8x+3y)^2-12^2\\ &=(8x+3y-12)(8x+3y+12). \end{aligned}$$
5. $$\begin{aligned} c^2-a^2+22a-121&=c^2-(a^2-22a+121)\\ &=c^2-(a-11)^2\\ &=(c-a+11)(c+a-11). \end{aligned}$$
6. $$\begin{aligned} 100-25y^2-60x^2y-36x^4&=100-(25y^2+60x^2y+36x^4)\\ &=10^2-(5y+6x^2)^2\\ &=(10-5y-6x^2)(10+5y+6x^2). \end{aligned}$$

Ответ

1) $$(m^2-2m-1)(m-1)^2$$
2) $$(4-4m-m^2)(m+2)^2$$
3) $$(x-9y-z)(x-9y+z)$$
4) $$(8x+3y-12)(8x+3y+12)$$
5) $$(c-a+11)(c+a-11)$$
6) $$(10-5y-6x^2)(10+5y+6x^2)$$