Question

СРОЧНО
Разложите на множители

1) 27a^3b^6+54a^2b^4c^2+36ab^2c^4+8c^6

2) x^9y^12+3x^3y^4z^4-3x^6y^8z^2-z^6

3) (a-b)(a^2-c^2)-(a-c)(a^2-b^2)

4) (x+y)^2-10(x^2-y^2)+25(x-y)^2

Answer 1

1) 27a³b⁶+54a²b⁴c²+36ab²c⁴+8c⁶=(3ab²+2c²)(3ab²+2c²)(3ab²+2c²)

2) x^9y^12+3x^3y^4z^4-3x^6y^8z^2-z^6 =(x³y⁴-z²)(x³y⁴-z²)(x³y⁴-z²)

3) (a-b)(a^2-c^2)-(a-c)(a^2-b^2) =(a-b)(a-c)(a+c)-(a-c)(a-b)(a+b)=(a-b)(a-c)(a+c-a-b)=(a-b)(a-c)(c-b)

4) (x+y)^2-10(x^2-y^2)+25(x-y)^2=(x+y-5(x-y))²=(x+y-5x+5y)²=(6y-4x)²=4(3y-2x)(3y-2x)