Упр.21.1 ГДЗ Мерзляк Поляков 7 класс (Алгебра)

1) 2a^2-2b^2; 2) cx^2-cy^2; 3) 3x^2-3;
4) 3ab^2-27a; 5) x^3-4x; 6) 2y^3-18y;
7) x^4-x^2; 8) 0,09t^4-t^6; 9) 16/49 a^2 b^4 c^5-b^2 c^3.

1. $$2a^2-2b^2=2(a^2-b^2)=2(a-b)(a+b)$$
2. $$cx^2-cy^2=c(x^2-y^2)=c(x-y)(x+y)$$
3. $$3x^2-3=3(x^2-1)=3(x-1)(x+1)$$
4. $$3ab^2-27a=3a(b^2-9)=3a(b-3)(b+3)$$
5. $$x^3-4x=x(x^2-4)=x(x-2)(x+2)$$
6. $$2y^3-18y=2y(y^2-9)=2y(y-3)(y+3)$$
7. $$x^4-x^2=x^2(x^2-1)=x^2(x-1)(x+1)$$
8. $$0{,}09t^4-t^6=t^4(0{,}09-t^2)=t^4(0{,}3-t)(0{,}3+t)$$
9. $$\frac{16}{49}a^2b^4c^5-b^2c^3=b^2c^3\left(\frac{16}{49}a^2b^2c^2-1\right)=b^2c^3\left(\frac{4}{7}abc-1\right)\left(\frac{4}{7}abc+1\right)$$

Ответ

1) $$2(a-b)(a+b)$$; 2) $$c(x-y)(x+y)$$; 3) $$3(x-1)(x+1)$$; 4) $$3a(b-3)(b+3)$$; 5) $$x(x-2)(x+2)$$; 6) $$2y(y-3)(y+3)$$; 7) $$x^2(x-1)(x+1)$$; 8) $$t^4(0{,}3-t)(0{,}3+t)$$; 9) $$b^2c^3\left(\frac{4}{7}abc-1\right)\left(\frac{4}{7}abc+1\right)$$.