\(a,x^2-5x=x\left(x-5\right)\)
\(b,x^2-10x+25-y^2=\left(x^2-10x+25\right)-y^2=\left(x-5\right)^2-y^2=\left(x-5-y\right).\left(x-5+y\right)\)
\(b,x^3+y^3-3x-3y=\left(x+y\right).\left(x^2+xy+y^2\right)-3.\left(x+y\right)\)
\(=\left(x+y\right).\left(x^2+xy+y^2-3\right)\)
\(d,x^3+2x^2y+xy^2-4x=x\left(x^2+2xy+y^2-4\right)\)
\(=x.\left(x+y-2\right).\left(x+y+2\right)\)
a)
\(x^2-5x=x\left(x-5\right)\)
b)
\(=\left(x^2-10x+25\right)-y^2=\left(x-5\right)^2-y^2=\left(x-5-y\right)\left(x-5+y\right)\)
c)
\(=\left(x^3+y^3\right)-\left(3x+3y\right)\)
\(=\left(x+y\right)\left(x^2-xy+y^2\right)-3\left(x+y\right)\)
\(=\left(x+y\right)\left(x^2-xy+y^2-3\right)\)
d)
\(=x\left(x^2+2xy+y^2-4\right)\)
\(=x\left[\left(x^2+2xy+y^2\right)-2^2\right]\)
\(=x\left[\left(x+y\right)-2^2\right]\)
\(=x\left(x+y-2\right)\left(x+y+2\right)\)
a/x2-5x=x(x-5)
b/x2-10x+25-y2=(x2-10+25)-y2=(x-5)2-y2=(x-5-y)(x-5+y)
