a) Ta có: \(ax-ay+bx-by\)
\(=a\left(x-y\right)+b\left(x-y\right)\)
\(=\left(x-y\right)\left(a+b\right)\)
b) Ta có: \(ax-ay+bx-by\)
\(=a\left(x-y\right)+b\left(x-y\right)\)
\(=\left(x-y\right)\left(a+b\right)\)
c) Ta có: \(x^2+xy+ax+ay\)
\(=x\left(x+y\right)+a\left(x+y\right)\)
\(=\left(x+y\right)\left(x+a\right)\)
d) Ta có: \(x^2y+xy^2-x-y\)
\(=xy\left(x+y\right)-\left(x+y\right)\)
\(=\left(x+y\right)\left(xy-1\right)\)
e) Ta có: \(x^2y-xy^2-5x+5y\)
\(=xy\left(x-y\right)-5\left(x-y\right)\)
\(=\left(x-y\right)\left(xy-5\right)\)
f) Ta có: \(2x^2+2xy-x-y\)
\(=2x\left(x+y\right)-\left(x+y\right)\)
\(=\left(x+y\right)\left(2x-1\right)\)
g) Ta có: \(x^2y-4x+xy^2-4y\)
\(=x\left(xy-4\right)+y\left(xy-4\right)\)
\(=\left(xy-4\right)\left(x+y\right)\)
h) Ta có: \(x^4+x^3+x+1\)
\(=x^3\left(x+1\right)+\left(x+1\right)\)
\(=\left(x+1\right)\left(x^3+1\right)\)
\(=\left(x+1\right)^2\cdot\left(x^2-x+1\right)\)
i) Ta có: \(x^4-x^3-x+1\)
\(=x^3\left(x-1\right)-\left(x-1\right)\)
\(=\left(x-1\right)\left(x^3-1\right)\)
\(=\left(x-1\right)^3\cdot\left(x^2+x+1\right)\)
j) Ta có: \(x^2+x-y^2+y\)
\(=\left(x-y\right)\left(x+y\right)+\left(x+y\right)\)
\(=\left(x+y\right)\left(x-y+1\right)\)
k) Ta có: \(4x^2-9y^2+4x-6y\)
\(=\left(2x-3y\right)\left(2x+3y\right)+2\left(2x-3y\right)\)
\(=\left(2x-3y\right)\left(2x+3y+2\right)\)
i) Ta có: \(x^2+x+2xy+y+y^2\)
\(=\left(x^2+2xy+y^2\right)+\left(x+y\right)\)
\(=\left(x+y\right)^2+\left(x+y\right)\)
\(=\left(x+y\right)\left(x+y+1\right)\)
m) ta có: \(16x^2-9-24xy+9y^2\)
\(=\left(16x^2-24xy+9y^2\right)-9\)
\(=\left(4x-3y\right)^2-9\)
\(=\left(4x-3y-3\right)\left(4x-3y+3\right)\)
n) Ta có: \(4x^2-4xy-1+y^2\)
\(=\left(4x^2-4xy+y^2\right)-1\)
\(=\left(2x-y\right)^2-1\)
\(=\left(2x-y-1\right)\left(2x-y+1\right)\)
o) Ta có: \(x^2-x-2xy+y+y^2\)
\(=\left(x^2-2xy+y^2\right)-\left(x-y\right)\)
\(=\left(x-y\right)^2-\left(x-y\right)\)
\(=\left(x-y\right)\left(x-y-1\right)\)
