Question

Phân tích đa thức thành nhân tử 

a) x²(x-2y)+5x(x-2y)

b)x²(x-1)+2x(x-1)+x-1

c)(x²+1)²-4x²

d)3(x+3)-x²+9

e)x⁴- 1/9x²

f)2x²-2xy-16x+16y

g) x³+4x²y-16x+4xy² 

Answer 1

a) \(=\left(x-2y\right)\left(x^2+5x\right)\)

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

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

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

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

d) \(=3\left(x+3\right)-\left(x-3\right)\left(x+3\right)\)

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

     \(=\left(x+3\right)\left(6-x\right)\)

e) \(=\left(x^2-\frac{1}{3}x\right)\left(x^2+\frac{1}{3}x\right)\)

f) \(=2x\left(x-y\right)-16\left(x-y\right)\)

    \(=2\left(x-y\right)\left(x-8\right)\)