Question

Phân tích đa thức thành nhân tử

a, 4a² - 4a + 1 - b²

b, 4x³ - 4x² - 9x + 9

Answer 1

a) \(4a^2-4a+1-b^2=\left(2a\right)^2-2.2.a+1-b^2\\ =\left(2a-1\right)-b^2=\left(2a-1+b\right)\left(2a-1-b\right)\)

b) \(4x^3-4x^2-9x+9=4x^2\left(x-1\right)-9\left(x-1\right)\\ =\left(x-1\right)\left(4x^2-3^2\right)=\left(x-1\right)\left(2x-3\right)\left(2x+3\right)\)

Answer 2

a) \(4a^2-4a+1-b^2\)

\(=\left(2a-1\right)^2-b^2\)

\(=\left(2a-b-1\right)\left(2a+b-1\right)\)

b) \(4x^3-4x^2-9x+9\)

\(=4x^2\left(x-1\right)-9\left(x-1\right)\)

\(=\left(4x^2-9\right)\left(x-1\right)\)

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