Question

Answer 1

 b)\(x^5-x^4y-xy^4+y^5=x^4\left(x-y\right)-y^4\left(x+y\right)=\left(x^4-y^4\right)\left(x-y\right)=\left(x^2-y^2\right)\left(x^2+y^2\right)\left(x-y\right)=\left(x-y\right)\left(x+y\right)\left(x^2+y^2\right)\left(x-y\right)=\left(x-y\right)^2\left(x+y\right)\left(x^2+y^2\right)\)

c)\(x^6y-x^4y^3-x^3y^4+xy^6=x^4y\left(x^2-y^2\right)-xy^4\left(x^2-y^2\right)=xy\left(x^3-y^3\right)\left(x^2-y^2\right)=xy\left(x-y\right)^2\left(x+y\right)\left(x^2+xy+y^2\right)\)

d)\(x^2-6xy+9y^2-9=\left(x-3y\right)^2-9=\left(x-3y-3\right)\left(x-3y+3\right)\)

e)\(25x^2-y^2+4y-4=25x^2-\left(y-2\right)^2=\left(5x-y+2\right)\left(5x+y-2\right)\)