Упр.17.12 ГДЗ Мерзляк Поляков 7 класс (Алгебра)

1) (-x+1)^2; 2) (-m-9)^2; 3) (-5a+3b)^2;
4) (-4x-8y)^2; 5) (-0,7c-10d)^2; 6) (-4a^2+1/8 ab)^2.

Используем формулу квадрата суммы:

$$ (u+v)^2=u^2+2uv+v^2. $$

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

2. $$(-m-9)^2=(-(m+9))^2=(m+9)^2=m^2+18m+81.$$

3. $$(-5a+3b)^2=(3b-5a)^2=9b^2-30ab+25a^2.$$

4. $$(-4x-8y)^2=(-(4x+8y))^2=(4x+8y)^2=16x^2+64xy+64y^2.$$

5. $$(-0{,}7c-10d)^2=(-(0{,}7c+10d))^2=(0{,}7c+10d)^2=0{,}49c^2+14cd+100d^2.$$

6. $$\left(-4a^2+\frac18ab\right)^2=\left(\frac18ab-4a^2\right)^2$$

   $$=\frac1{64}a^2b^2-a^3b+16a^4.$$

Ответ

1) $$1-2x+x^2$$; 2) $$m^2+18m+81$$; 3) $$9b^2-30ab+25a^2$$; 4) $$16x^2+64xy+64y^2$$; 5) $$0{,}49c^2+14cd+100d^2$$; 6) $$\frac1{64}a^2b^2-a^3b+16a^4$$.