Question

Phân tích đa thức thành nhân tử
1) y² - 4y + 4 - x²
2) 8x³ -12x² + 6x - 2

Answer 1

1)

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

2)

\(8x^3-12x^2+6x-2\\ =2\left(4x^3-6x^2+3x-1\right)\\ =2\left(4x^3-4x^2-2x^2+2x+x-1\right)\\ =2\left(4x^2\left(x-1\right)-2x\left(x-1\right)+\left(x-1\right)\right)\\ =2\left(x-1\right)\left(4x^2-2x+1\right)\)

Answer 2

1) \(y^2-4y+4-x^2\)

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

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

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

2) \(8x^3-12x^2+6x-1\)

\(=\left(2x\right)^3-3\cdot\left(2x\right)^2\cdot1+3\cdot2x\cdot1^2-1^3\)

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

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