Question

Answer 1

\(a,=5xy\left(x+2\right)\\ b,=\left(x-y\right)^2-25=\left(x-y-5\right)\left(x-y+5\right)\\ c,=\left(x-2\right)\left(x^2+2x+4\right)+2x\left(x-2\right)\\ =\left(x-2\right)\left(x^2+4x+4\right)=\left(x-2\right)\left(x+2\right)^2\\ d,=x^4+2x^2y^2+y^4-x^2y^2=\left(x^2+y^2\right)^2-x^2y^2\\ =\left(x^2-xy+y^2\right)\left(x^2+xy+y^2\right)\)

Answer 2

\(a,5x^2y+10xy=5xy\left(x+2\right)\)

\(b,x^2-2xy+y^2-25=\left(x^2-2xy+y^2\right)-5^2=\left(x-y\right)^2-5^2=\left(x-y+5\right)\left(x-y-5\right)\)

\(c,x^3-8+2x\left(x-2\right)\\ =\left(x-2\right)\left(x^2+2x+4\right)+2x\left(x-2\right)\\ =\left(x-2\right)\left(x^2+2x+4+2x\right)\\ =\left(x-2\right)\left(x^2+4x+4\right)\\ =\left(x-2\right)\left(x+2\right)^2\)

 

Answer 3

\(a,5x^2y+10xy=5xy\left(x+2\right)\)

\(b,x^2-2xy+y^2-25=\left(x-y\right)^2-5^2=\left(x-y-5\right)\left(x-y+5\right)\)

\(c,x^3-8+2x\left(x-2\right)=\left(x-2\right)\left(x^2+2x+4\right)+2x\left(x-2\right)=\left(x-2\right)\left(x^2+2x+4+2x\right)=\left(x-2\right)\left(x+2\right)^2=\left(x-2\right)\left(x+2\right)\left(x+2\right)\)

\(d,x^4+x^2y^2+y^4=x^4+2x^2y^2+y^4-x^2y^2=\left[\left(x^2\right)^2+2x^2y^2+\left(y^2\right)^2\right]-\left(xy\right)^2\)

=\(\left(x^2+y^2\right)^2-\left(xy\right)^2=\left(x^2+y^2-xy\right)\left(x^2+y^2+xy\right)\)