A little Calculus Help?

Question

ok. i'm not looking for an easy way out, i just need someone to explain how to do these. thank youuuu in advance =)

Factor: x^4 - y^4 + x^3 - xy^2

Divide: (3x^2 + 4x - 17) by (x^2 - 6x +10)

Answer 1

x^4 - y^4 + x^3 - xy^2  ... Start with the given expression.

(x^4 - y^4) + (x^3 - xy^2) ... Pair up the terms

(x^2 - y^2)(x^2 + y^2) + (x^3 - xy^2) ... Factor the first group with the use of difference of squares.

(x-y)(x+y)(x^2 + y^2) + (x^3 - xy^2) ... Factor again with the use of difference of squares.

(x-y)(x+y)(x^2 + y^2) + x(x^2 - y^2) ... Factor out the GCF "x" from the second group

(x-y)(x+y)(x^2 + y^2) + x(x-y)(x+y) ... Factor with the use of difference of squares.

(x-y)(x+y)(x^2+x+y^2) ... Factor out the GCF (x-y)(x+y)

So x^4 - y^4 + x^3 - xy^2 factors to (x-y)(x+y)(x^2+x+y^2)

Answer 2

x^4 - y^4 + x^3 - xy^2

solution...

(x - y)^4 + x(x^2 -y^2)...

(x - y)^4 + x(x - y)^2...

each quantity is an example of the special binary products...