Упр.384 ГДЗ Муравин 7 класс (Алгебра)

1) (x + 3)^2 — 1; 4) x^2 — (2x — 1)^2;
2) 64 — (b + 1)^2; 5) (y — 1)^2 — (5y — 7)^2;
3) (4a — 3)^2 — 16; 6) (a — 1)^2 — (a + 1)^2.

1. $$ (x+3)^2-1=(x+3)^2-1^2=((x+3)-1)((x+3)+1)=(x+2)(x+4) $$
2. $$ 64-(b+1)^2=8^2-(b+1)^2=(8-(b+1))(8+(b+1))=(7-b)(9+b) $$
3. $$ (4a-3)^2-16=(4a-3)^2-4^2=((4a-3)-4)((4a-3)+4)=(4a-7)(4a+1) $$
4. $$ x^2-(2x-1)^2=(x-(2x-1))(x+(2x-1))=(x-2x+1)(x+2x-1)=(1-x)(3x-1) $$
5. $$ (y-1)^2-(5y-7)^2=((y-1)-(5y-7))((y-1)+(5y-7)) $$
   $$ =(y-1-5y+7)(y-1+5y-7)=(6-4y)(6y-8) $$
6. $$ (a-1)^2-(a+1)^2=((a-1)-(a+1))((a-1)+(a+1)) $$
   $$ =(a-1-a-1)(a-1+a+1)=-2\cdot 2a=-4a $$

Ответ

1) $$ (x+2)(x+4) $$
2) $$ (7-b)(9+b) $$
3) $$ (4a-7)(4a+1) $$
4) $$ (1-x)(3x-1) $$
5) $$ (6-4y)(6y-8) $$
6) $$ -4a $$