Lời giải:
$x^2-x-y^2-y=(x^2-y^2)-(x+y)=(x-y)(x+y)-(x+y)=(x+y)(x-y-1)$
$x^2-y^2+x-y=(x^2-y^2)+(x-y)=(x-y)(x+y)+(x-y)=(x-y)(x+y+1)$
$3x-3y+x^2-y^2=(3x-3y)+(x^2-y^2)=3(x-y)+(x-y)(x+y)=(x-y)(3+x+y)$
$5x-5y+x^2-y^2=(5x-5y)+(x^2-y^2)=5(x-y)+(x-y)(x+y)=(x-y)(5+x+y)$
$x^2-y^2+2x-2y=(x^2-y^2)+(2x-2y)=(x-y)(x+y)+2(x-y)=(x-y)(x+y+2)$
$x^2-4y^2+x+2y=(x^2-4y^2)+(x+2y)=(x-2y)(x+2y)+(x+2y)=(x+2y)(x-2y+1)$
$x^2-y^2-2x-2y=(x^2-y^2)-(2x+2y)=(x-y)(x+y)-2(x+y)=(x+y)(x-y-2)$
$x^2-4y^2+2x+4y=(x^2-4y^2)+(2x+4y)=(x-2y)(x+2y)+2(x+2y)=(x+2y)(x-2y+2)$
\(x^2-x-y^2-y\)
\(=\left(x^2-y^2\right)-\left(x+y\right)\)
\(=\left(x-y\right)\left(x+y\right)-\left(x+y\right)\)
\(=\left(x+y\right)\left(x-y-1\right)\)
\(---\)
\(5x-5y+x^2-y^2\)
\(=\left(5x-5y\right)+\left(x^2-y^2\right)\)
\(=5\left(x-y\right)+\left(x-y\right)\left(x+y\right)\)
\(=\left(x-y\right)\left(5+x+y\right)\)
\(=\left(x-y\right)\left(x+y+5\right)\)
\(---\)
\(x^2-4y^2+x+2y\)
\(=\left(x^2-4y^2\right)+\left(x+2y\right)\)
\(=\left(x-2y\right)\left(x+2y\right)+\left(x+2y\right)\)
\(=\left(x+2y\right)\left(x-2y+1\right)\)
\(---\)
\(x^2-y^2+x-y\)
\(=\left(x^2-y^2\right)+\left(x-y\right)\)
\(=\left(x-y\right)\left(x+y\right)+\left(x-y\right)\)
\(=\left(x-y\right)\left(x+y+1\right)\)
\(---\)
\(x^2-5x-y^2-5y\)
\(=\left(x^2-y^2\right)-\left(5x+5y\right)\)
\(=\left(x-y\right)\left(x+y\right)-5\left(x+y\right)\)
\(=(x+y)(x-y-5)\)
\(---\)
\(x^2-y^2-2x-2y\)
\(=(x^2-y^2)-(2x+2y)\)
\(=(x-y)(x+y)-2(x+y)\)
\(=(x+y)(x-y-2)\)
#\(Toru\)
\(3x-3y+x^2-y^2\)
\(=\left(3x-3y\right)+\left(x^2-y^2\right)\)
\(=3\left(x-y\right)+\left(x-y\right)\left(x+y\right)\)
\(=\left(x-y\right)\left(3+x+y\right)\)
\(---\)
\(x^2-y^2+2x-2y\)
\(=\left(x^2-y^2\right)+\left(2x-2y\right)\)
\(=\left(x-y\right)\left(x+y\right)+2\left(x-y\right)\)
\(=\left(x-y\right)\left(x+y+2\right)\)
\(---\)
\(x^2-4y^2+2x+4y\)
\(=\left(x^2-4y^2\right)+\left(2x+4y\right)\)
\(=\left(x-2y\right)\left(x+2y\right)+2\left(x+2y\right)\)
\(=\left(x+2y\right)\left(x-2y+2\right)\)
