Question

Please simplify the following. Please show solution if possible:)

Question 1:
(x^3 + x^2 - y^3 - y^2) / (x^2 - 2xy + y^2)

Question 2:
(u^6 + v^6 + 2u^3 • v^3) / [u^3 - v^3 + (u^2 • v) - (u • v^2)]

Answer 1

clearly this is an exercise in factoring polynomials, so you can cancel common factors.

x^3 + x^2 - y^3 - y^2
= (x^3-y^3) + (x^2-y^2)
= (x-y)(x^2+xy+y^2) + (x-y)(x+y)

x^2-2xy+y^2 = (x-y)^2

u^6 + v^6 + 2u^3 • v^3 = (u^3+v^3)^2
= (u+v)^2 (u^2-uv+v^2)^2

u^3 - v^3 + (u^2 • v) - (u • v^2)
= u^3+u^2v - v^3-uv^2
= u^2(u+v) - v^2(u+v)
= (u^2-v^2)(u+v)
= (u-v)(u+v)^2

see what you can do with that...