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\(=\left(x-y\right)\left(x+y\right)-10\left(x+y\right)=\)
\(=\left(x+y\right)\left(x-y-10\right)\)
= (x - y). (x + y) - 10 ( x - y)
= [( x + y) - 10)] . ( x - y)
\(x^2-4x-y^2+4=\left(x^2-4x+4\right)-y^2=\left(x-2\right)^2-y^2=\left(x-2-y\right)\left(x-2+y\right)\)
\(=x^2+x+3x+3=x\left(x+1\right)+3\left(x+1\right)=\left(x+1\right)\left(x+3\right)\)
\(x^2-2xy+y^2+3x-3y-4\)
\(=\left(x-y\right)^2-1+3x-3y-3\)
\(=\left[\left(x-y\right)^2-1^2\right]+\left(3x-3y-3\right)\)
\(=\left[\left(x-y\right)-1\right]\left[\left(x-y\right)+1\right]+3\left(x-y-1\right)\)
\(=\left(x-y-1\right)\left(x-y+1\right)+3\left(x-y-1\right)\)
\(=\left(x-y-1\right)\left[\left(x-y+1\right)+3\right]\)
\(=\left(x-y-1\right)\left(x-y+4\right)\)
\(x^2+4xy+4y^2-25\)
\(=\left(x^2+4xy+4y^2\right)-25\)
\(=\left(x+2y\right)^2-5^2\)
\(=\left(x+2y+5\right)\left(x+2y-5\right)\)
\(x^2-y^2+10x-10y=\left(x-y\right)\left(x+y\right)+10\left(x-y\right)=\left(x-y\right)\left(x+y+10\right)\)