Question

Phân tích thành nhân tử

\((5x-10)(x^2 -1)-(3x-6)(x^2 -2x+1)\)

Answer 1

\(\left(5x-10\right)\left(x^2-1\right)-\left(3x-6\right)\left(x^2-2x+1\right)\)

\(=\left(5x-10\right)\left(x-1\right)\left(x+1\right)-\left(3x-6\right)\left(x-1\right)^2\)

\(=\left(x-1\right)\left[\left(5x-10\right)\left(x+1\right)-\left(3x-6\right)\left(x-1\right)\right]\)

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

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

\(=\left(x-1\right)\left[\left(x-2\right)\left(2x+8\right)\right]\)

\(=\left(x-1\right)\left(x-2\right)\left(2x+8\right)\)