Упр.16.9 ГДЗ Мерзляк Поляков 7 класс (Алгебра)

1) (x-2)^2-4; 4) a^4-(7b-a^2 )^2;
2) (b+7)^2-100c^2; 5) (4x-9)^2-(2x+19)^2;
3) 121-(b+7)^2; 6) (a+b+c)^2-(a-b-c)^2.

1. $$\begin{aligned} (x-2)^2-4&=(x-2)^2-2^2\\ &=(x-2-2)(x-2+2)\\ &=(x-4)x \end{aligned}$$
2. $$\begin{aligned} (b+7)^2-100c^2&=(b+7)^2-(10c)^2\\ &=(b+7-10c)(b+7+10c) \end{aligned}$$
3. $$\begin{aligned} 121-(b+7)^2&=11^2-(b+7)^2\\ &=(11-(b+7))(11+(b+7))\\ &=(4-b)(b+18) \end{aligned}$$
4. $$\begin{aligned} a^4-(7b-a^2)^2&=(a^2)^2-(7b-a^2)^2\\ &=(a^2-(7b-a^2))(a^2+(7b-a^2))\\ &=(2a^2-7b)(7b) \end{aligned}$$
5. $$\begin{aligned} (4x-9)^2-(2x+19)^2&=\bigl((4x-9)-(2x+19)\bigr)\bigl((4x-9)+(2x+19)\bigr)\\ &=(2x-28)(6x+10)\\ &=2(x-14)\cdot 2(3x+5)\\ &=4(x-14)(3x+5) \end{aligned}$$
6. $$\begin{aligned} (a+b+c)^2-(a-b-c)^2&=\bigl((a+b+c)-(a-b-c)\bigr)\bigl((a+b+c)+(a-b-c)\bigr)\\ &=(2b+2c)\cdot 2a\\ &=4a(b+c) \end{aligned}$$

Ответ

1) $$x(x-4)$$;
2) $$(b+7-10c)(b+7+10c)$$;
3) $$(4-b)(b+18)$$;
4) $$7b(2a^2-7b)$$;
5) $$4(x-14)(3x+5)$$;
6) $$4a(b+c)$$.