Phân tích đa thức thành nhân tử:
1) \(5x^2-5xy-10x+10y\)
2) \(25-a^2-2ab-b^2\)
3) \(a^2x^2-a^2y^2-b^2x^2+b^2y^2\)
4) \(x^2-y^2+12y-36\)
5) \(16x^2-y^2\)
6) \(1+27x^3\)
7) \(x^3-x^2-x+1\)
8) \(4x\left(x-3y\right)+12y\left(3y-x\right)\)
9) \(x^2-2xy+y^2+3x-3y-10\)
10) \(4x\left(x+1\right)^2-5x^2\left(x+1\right)-4\left(x+1\right)\)
a, = 5x(x-y)-10(x-y)
=(5x-10)(x-y)
=5(x-2)(x-y)
b, 25-a2-2ab-b2
= 52-(a+b)2
=(5-a-b)(5+a+b)
c, a2x2-a2y2-b2x2+b2y2
=a2(x2-y2)-b2(x2-y2)
=(a-b)(a+b)(x-y)(x+y)
d,
e, 16x2-y2
=(4x-y)(4x+y)
f, 1+27x3
= (1+3x)(1-3x+9x2)
g, x3-x2-x+1
=x2(x-1)-(x-1)
=(x2-1)(x-1)
=(x-1)(x+1)(x-1)
h, 4x(x-3y)+12y(3y-x)
=4x(x-3y)-12y(x-3y)
=(4x-12y)(x-3y)
=4(x-3y)2
l, x2-2xy+y2+3x-3y-10
=(x-y)2+3(x-y)-10
=(x-y)(x-y+3)-10
k, 4x(x+1)2-5x2(x+1)-4(x+1)
=(4x2+4x-5x2-4)(x+1)
=-(x-2)2(x+1)
