Question

Phân tích các đa thức sau thành nhân tử :

a) \(a^2-b^2-4a+4\)

b) \(x^2+2x-3\)

c) \(4x^2y^2-\left(x^2+y^2\right)^2\)

d) \(2a^3-54b^3\)

Answer 1

Answer 2

a) $a^2-b^2-4a+4$

$\mathrm{=(a2-4a+4)-b2}$

$\mathrm{=(a-2)2-b2}$

$\mathrm{=(a-2-b)(a-2+b)}$

b) $x^2+2x-3$

$\mathrm{=x2-x+3x-3}$

$\mathrm{=x(x-1)+3(x-1)}$

$\mathrm{=(x+3)(x-1)}$

c) $4x^2{y}^2-{\left(x^2+y^2\right)}^2$

=(2xy-x²-y²)(2xy+x²+y²)

=-(x-y)²(x+y)²

d) $2a^3-54b^3$

=2(a³-27b³)

=2(a-3b)(a2+3ab+9b2)