Question

Prove that
x² + y² = (x+y) (xw + yw^2) (xw^2 + yw)​

Answer 1

Answer:

x³+y³=(x+y)(xω+yω²)(xω²+yω)

Step-by-step explanation:

RHS=(x+y)(xω+yω²)(xω²+yω)

=(x+y)(xω-y-yω)(-x-xω+yω) [ ⁰₀⁰ 1+ω+ω²=0]

=(x+y)(-x²ω-x²ω²+xyω²+xy+xyω-y²ω+xyω+xyω²-y²ω²)

=(x+y)(-x²ω+x²+x²ω-xy-xyω+xy+xyω-y²ω+xyω-xy-xyω+y²+y²ω)

=(x+y)(x²-xy+y²)

=x³+y³