Question

Разложите на множители: 1) -6x^2+12x-6; 2) 9xy-27xy^3+54x^2y; 3) 25x^2-y^2; 4) 24x^2-168x+296.

Answer 1

1)

$\displaystyle \tt -6x^2+12x-6=-6(x^2-2x+1)=-6(x-1)^2=\bold{-6(x-1)(x-1)}$

2)

$\displaystyle \tt 9xy-27xy^3+54x^2y=\bold{9xy(1-3y^2+6x)}$

3)

$\displaystyle \tt 25x^2-y^2=5^2x^2-y^2=(5x)^2-y^2=\bold{(5x-y)(5x+y)}$

4)

$\displaystyle \tt 24x^2-168x+296=\bold{8(3x^2-21x+37)}$