Question

Phân tích đa thức thành nhân tử:

a) 3x(x+1)²-5x²(x+1)+7(x+1)

b)(2x+1)²-(x-1)²

c)9(x+5)²-(x-7)²

Answer 1

Câu a :

\(3x\left(x+1\right)^2-5x^2\left(x+1\right)+7\left(x+1\right)\)

\(=\left(x+1\right)\left(-2x^2+3x+7\right)\)

Câu b :

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

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

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

Câu c :

\(9\left(x+5\right)^2-\left(x-7\right)^2\)

\(=\left(3x+15\right)^2-\left(x-7\right)^2\)

\(=\left(3x+15-x+7\right)\left(3x+15+x-7\right)\)

\(=\left(2x+22\right)\left(4x+8\right)\)

\(=8\left(x+11\right)\left(x+2\right)\)