Question

Разложите на множители 

1. 12a²b-27b³

2. -40x³-120x²y-90xy²

3. 2a⁴-16ab³

4. (x³+8)-(3x+6)

 

Answer 1

 

$<var>1) \ 12a^2b-27b^3 = b(12a^2-27b^2) =\\\\3b(4a^2-9b^2) = 3b(2a-3b)(2a+3b)\\\\ 2) \ -40x^3-120x^2y-90xy^2 = -10x(4x^2+12xy+9y^2) =\\\\ -10x(2x+3y)^2\\\\ 3) \ 2a^4-16ab^3 = 2a(a^3-8b^3) = 2a(a-2b)(a^2+2ab+4b^2)\\\\ 4) \ (x^3+8)-(3x+6) =\\\\ x^3-3x+2= x^3 - x^2 + x^2 - x - 2x + 2 =\\\\ x^2(x-1)+x(x-1)-2(x-1) = (x-1)(x^2+x-2) =\\\\(x-1)(x^2-x+2x-2) = (x-1)(x(x-1)+2(x-1)) =\\\\ (x-1)(x-1)(x+2) </var>$