Question

Phân tích các đa thức sau thành nhân tử

a) 4x²-9y²+6x-9y

b) 1-2x+2yz+x²-y²-z²

c) x³-1+5x²-5+3x-3

Answer 1

a)

\(4x^2-9y^2+6x-9y=\left(2x-3y\right)\left(2x+3\right)+3\left(2x-3y\right)\)

\(=\left(2x-3y\right)\left(2x+3y+3\right)\)

b)

\(1-2x+2yz+x^2-y^2-z^2=\left(x^2-2x+1\right)-\left(y^2-2yz+z^2\right)\) (đổi dấu)

\(=\left(x-1\right)^2-\left(y-z\right)^2\)

c)

\(x^3-1+5x^2-5+3x-3=\left(x-1\right)\left(x^2+x+1\right)+5\left(x-1\right)\left(x+1\right)+3\left(x-1\right)\)

\(=\left(x-1\right)\left(x^2+x+1+5\left(x+1\right)+3\right)\)

\(=\left(x-1\right)\left(x^2+x+1+5x+5+3\right)\)

\(=\left(x-1\right)\left(x^2+6x+9\right)=\left(x-1\right)\left(x+3\right)^2\)

Answer 2

(2x-3y)(2x+3y) chớ x + 3 k ik