Bài 4 : Phân tích đa thức thành nhân tử :
c, x\(^2\) - x + 2y - 4y\(^2\)
d, x\(^3\) - x + 2y - 8y\(^3\)
e, 2x\(^3\) - 8x\(^2\) - 24x + 54
f, x\(^2\) - 6x + 9 - y\(^2\)
g, 25 - 4x\(^2\) - 4xy - y\(^2\)
h, 4x\(^2\) - y\(^2\) + 4y - 4
i, x\(^2\) - 4xy + 4y\(^2\) + xz - 2yz
j, x\(^2\) + 2xy + y\(^2\) - xz - yz
k, x\(^3\) + y\(^3\) + x + y
l, x\(^3\) - y\(^3\) + x - y
m, ( x - y )\(^3\) + x\(^2\) - y\(^2\)
c: \(x^2-x+2y-4y^2\)
\(=\left(x^2-4y^2\right)-\left(x-2y\right)\)
=(x-2y)(x+2y)-(x-2y)
=(x-2y)(x+2y-1)
d: \(x^3-x+2y-8y^3\)
\(=\left(x^3-8y^3\right)-\left(x-2y\right)\)
\(=\left(x-2y\right)\left(x^2+2xy+4y^2\right)-\left(x-2y\right)\)
\(=\left(x-2y\right)\left(x^2+2xy+4y^2-1\right)\)
e: \(2x^3-8x^2-24x+54\)
\(=2\left(x^3-4x^2-12x+27\right)\)
\(=2\left(x^3+3x^2-7x^2-21x+9x+27\right)\)
\(=2\left(x+3\right)\left(x^2-7x+9\right)\)
f: \(x^2-6x+9-y^2\)
\(=\left(x-3\right)^2-y^2\)
=(x-3-y)(x-3+y)
g: \(25-4x^2-4xy-y^2\)
\(=25-\left(4x^2+4xy+y^2\right)\)
\(=25-\left(2x+y\right)^2\)
=(5-2x-y)(5+2x+y)
h: \(4x^2-y^2+4y-4\)
\(=4x^2-\left(y^2-4y+4\right)\)
\(=\left(2x\right)^2-\left(y-2\right)^2\)
\(=\left(2x-y+2\right)\left(2x+y-2\right)\)
i: \(x^2-4xy+4y^2+xz-2yz\)
\(=\left(x-2y\right)^2+z\left(x-2y\right)\)
=(x-2y)(x-2y+z)
j: \(x^2+2xy+y^2-xz-yz\)
\(=\left(x+y\right)^2-z\left(x+y\right)\)
=(x+y)(x+y-z)
k: \(x^3+y^3+x+y\)
\(=\left(x^3+y^3\right)+\left(x+y\right)\)
\(=\left(x+y\right)\left(x^2-xy+y^2\right)+\left(x+y\right)\)
\(=\left(x+y\right)\left(x^2-xy+y^2+1\right)\)
l: \(x^3-y^3+x-y\)
\(=\left(x^3-y^3\right)+\left(x-y\right)\)
\(=\left(x-y\right)\left(x^2+xy+y^2\right)+\left(x-y\right)\)
\(=\left(x-y\right)\left(x^2+xy+y^2+1\right)\)
m: \(\left(x-y\right)^3+x^2-y^2\)
\(=\left(x-y\right)^3+\left(x-y\right)\left(x+y\right)\)
\(=\left(x-y\right)\left[\left(x-y\right)^2+x+y\right]\)