Question

Phân tích các đa thức sau thành nhân tử ; a) x^2+6x+9 b) 4x-1-4x^2 c) 1-9x^2 d) (2x+y)^2-4x^2+12x-9 e) 9-6x+x^2-y^2 f) x^3+6x^2+12x+8 g) x^3-6x^2y+12xy^2+8y^3

Answer 1

a: \(=\left(x-3\right)^2\)

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

c: \(=\left(1-3x\right)\left(1+3x\right)\)

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

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

\(=\left(4x+y-3\right)\cdot\left(y+3\right)\)

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

f: \(=\left(x+2\right)^3\)

g: \(=\left(x-2y\right)^3\)

Answer 2

\(a,=\left(x+3\right)^2\\ b,=-\left(2x-1\right)^2\\ c,=\left(3x-1\right)\left(3x+1\right)\\ d,=\left(2x+y\right)^2-\left(2x-3\right)^2\\ =\left(2x+y-2x+3\right)\left(2x+y+2x-3\right)\\ =\left(y+3\right)\left(4x+y-3\right)\\ e,=\left(x-3\right)^2-y^2\\ =\left(x-3-y\right)\left(x-3+y\right)\\ f,=\left(x+2\right)^3\\ g,=\left(x-2y\right)^3\)