Question

Bài 1:Thực hiện phép tính

(4x - 1)(2x² - x - 1)

Bài 2:Rút gọc các biểu thức sau:

a) (x + 1)² + (x - 2)(x + 2) - 3(x+1)

b) (3x + 1)² + 2(3x + 1)(2x - 1) + (2x - 1)²

Bài 3:Phân tích đa thức thành phân tử

a) x² - 2x + x³

b) 2x² - 5x³ - x

Answer 1

1.\(\left(4x-1\right)\left(2x^2-x-1\right)\)

\(=8x^3-4x^2-4x-2x^2+x+1\)

\(=8x^3-6x^2-3x+1\)

2.a)\(\left(x+1\right)^2+\left(x-2\right)\left(x+2\right)-3\left(x+1\right)\)

\(=x^2+2x+1+x^2-4-3x-3\)

\(=2x^2-x-6\)

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

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

\(=\left(5x\right)^2=25x^2\)

3.a)\(x^2-2x+x^3\)

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

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

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

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

b)\(2x^2-5x^3-x\)

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