Упр.12.3 ГДЗ Мерзляк Поляков 7 класс (Алгебра)

1. 12.3. Упростите выражение:
   
   1) $$(x+2)(x+11)-2x(3-4x)$$;
   
   2) $$(a+5)(a-2)+(a-4)(a+6)$$;
   
   3) $$(y-9)(3y-1)-(2y+1)(5y-7)$$;
   
   4) $$(4x-1)(4x-3)-(2x-10)(8x+1)$$.

1. $$\begin{aligned} (x+2)(x+11)-2x(3-4x) &= x^2+11x+2x+22-6x+8x^2 \\ &= 9x^2+7x+22. \end{aligned}$$

2. $$\begin{aligned} (a+5)(a-2)+(a-4)(a+6) &= a^2-2a+5a-10+a^2+2a-24 \\ &= 2a^2+5a-34. \end{aligned}$$

3. $$\begin{aligned} (y-9)(3y-1)-(2y+1)(5y-7) &= 3y^2-y-27y+9-(10y^2-14y+5y-7) \\ &= 3y^2-28y+9-10y^2+9y+7 \\ &= -7y^2-19y+16. \end{aligned}$$

4. $$\begin{aligned} (4x-1)(4x-3)-(2x-10)(8x+1) &= 16x^2-12x-4x+3-(16x^2+2x-80x-10) \\ &= 16x^2-16x+3-16x^2+78x+10 \\ &= 62x+13. \end{aligned}$$

Ответ

1) $$9x^2+7x+22$$; 2) $$2a^2+5a-34$$; 3) $$-7y^2-19y+16$$; 4) $$62x+13$$.