Question

(a+b) +(aw+bw^2)+(aw^2+bw)=0​

Answer 1

Step-by-step explanation:

How is (a+b) (aw+bw^2) (aw^2+bw) = (a^3+b^3)?

If a= -b this is clearly true for any w. Suppose a ≠ -b; then you can divide both sides by (a+b), resulting in:

a2w3+b2w3+abw4+abw2=a2−ab+b2

Comparing coefficients for a2,b2,ab between LHS and RHS, we note that the identity holds if, simultaneously, w3=1 and w4+w2=−1

⟹w×1+w2=−1⟹w2+w+1=0⟹w=−1±i3–√2