Question

Phân tích các đa thức sau thành nhân tử

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

9(2x+3)^2-4(x+1)^2

(4x^2-3x-18)^2 - (4x^2+3x)^2

-4x^2+12xy-9y^2+25

9(x+y-1)^2 -4(2x+3y+1)^2

Answer 1

a: \(=\left(3x+1\right)^2-\left(2x-4\right)^2\)

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

\(=\left(x+5\right)\left(5x-3\right)\)

b: \(=\left(6x+9\right)^2-\left(2x+2\right)^2\)

\(=\left(6x+9+2x+2\right)\left(6x+9-2x-2\right)\)

\(=\left(8x+11\right)\left(4x+7\right)\)

c: \(=\left(4x^2-3x-18-4x^2-3x\right)\left(4x^2-3x-18+4x^2+3x\right)\)

\(=\left(-6x-18\right)\left(8x^2-18\right)\)

\(=-6\cdot2\cdot\left(x+3\right)\left(4x^2-9\right)\)

\(=-12\left(x+3\right)\left(2x-3\right)\left(2x+3\right)\)