Упр.39.20 Часть 2 ГДЗ Мордкович Семенов 7 класс (Алгебра)

а) 81 — (a — 2)^2; г) 36 — (5 + x)^2;
б) x^2 — (2x — 1)^2; д) 4b^2 — (2 — b)^2;
в) 100x^2 — (5x + 9)^2; е) 121b^2 — (7b — 3)^2.

1. $$81-(a-2)^2=9^2-(a-2)^2=(9-(a-2))(9+(a-2))=(11-a)(7+a)$$

2. $$x^2-(2x-1)^2=(x-(2x-1))(x+(2x-1))=(1-x)(3x-1)$$

3. $$100x^2-(5x+9)^2=(10x)^2-(5x+9)^2=(10x-(5x+9))(10x+(5x+9))$$

   $$=(5x-9)(15x+9)=3(5x-9)(5x+3)$$

4. $$36-(5+x)^2=6^2-(5+x)^2=(6-(5+x))(6+(5+x))=(1-x)(11+x)$$

5. $$4b^2-(2-b)^2=(2b)^2-(2-b)^2=(2b-(2-b))(2b+(2-b))$$

   $$=(3b-2)(b+2)$$

6. $$121b^2-(7b-3)^2=(11b)^2-(7b-3)^2=(11b-(7b-3))(11b+(7b-3))$$

   $$=(4b+3)(18b-3)=3(4b+3)(6b-1)$$

Ответ

а) $$(11-a)(7+a)$$; б) $$(1-x)(3x-1)$$; в) $$3(5x-9)(5x+3)$$; г) $$(1-x)(11+x)$$; д) $$(3b-2)(b+2)$$; е) $$3(4b+3)(6b-1)$$.