Question

phân tích các đa thức thành nhân tử

a) 4x² + 4x + 1

b) x² - 6x - 9y^{2 + 9}

c) 12x - 9 - 4x²

d) 1 - 9x + 27x² - 27x³

Answer 1

a) Ta có: \(4x^2+4x+1\)

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

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

b) Sửa đề: \(x^2-6x+9-9y^2\)

Ta có: \(x^2-6x+9-9y^2\)

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

\(=\left(x-3-3y\right)\left(x-3+3y\right)\)

c) Ta có: \(12x-9-4x^2\)

\(=-\left(4x^2-12x+9\right)\)

\(=-\left[\left(2x\right)^2-2\cdot2x\cdot3+3^2\right]\)

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

d) Ta có: \(1-9x+27x^2-27x^3\)

\(=1^3-3\cdot1^2\cdot3x+3\cdot1\cdot\left(3x\right)^2-\left(3x\right)^3\)

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