Bài 1: Phân tích đa thức thành nhân tử:
a) a2x + a2y - 9x - 9y
b) x2 - x - 12
c) x2 (x-3) + 12 - 4x
d) 4x (x-y) + 6y (x-y)
e) 5 (x+y) - xy - y2
f) 2x2 - 5x - 3
g) 2x2 - 8xy
h) 10a2 + ab - 3b2
i) x2 - x - 6
k) 5x (x-y) - 15x + 15y
l) x (x-y) - 5x + 5y
m) x3 - 2x2 + x - xy2
n) x2 (2y-1) - 9 (2y-1)
o) 2x2 - 6x
p) 6xy - 2y
q) 3x2 - 3xy - x + y
r) x (x-1) + 1 - x
s) y (x-3) - x + 3
t) 5 (x-1) - 3x (x-1)
u) 2x (x+y) + x2 - y2
v) x3 - 8x2 + 7x
w) x5 - x3 + x2 - 1
a) \(a^2x+a^2y-9x-9y\)
\(=\left(a^2x+a^2y\right)-\left(9x+9y\right)\)
\(=a^2\left(x+y\right)-9\left(x+y\right)\)
\(=\left(x+y\right)\left(a^2-9\right)\)
\(=\left(x+y\right)\left(a-3\right)\left(a+3\right)\)
b) \(x^2-x-12\)
\(=x^2-4x+3x-12\)
\(=\left(x^2-4x\right)+\left(3x-12\right)\)
\(=x\left(x-4\right)+3\left(x-4\right)\)
\(=\left(x-4\right)\left(x+3\right)\)
c) \(x^2\left(x-3\right)+12-4x\)
\(=x^2\left(x-3\right)-\left(4x-12\right)\)
\(=x^2\left(x-3\right)-4\left(x-3\right)\)
\(=\left(x-3\right)\left(x^2-4\right)\)
\(=\left(x-3\right)\left(x-2\right)\left(x+2\right)\)
d) \(4x\left(x-y\right)+6y\left(x-y\right)\)
\(=\left(x-y\right)\left(4x+6y\right)\)
\(=2\left(x-y\right)\left(2x+3y\right)\)
e) \(5\left(x+y\right)-xy-y^2\)
\(=5\left(x+y\right)-\left(xy+y^2\right)\)
\(=5\left(x+y\right)-y\left(x+y\right)\)
\(=\left(x+y\right)\left(5-y\right)\)
