Question

simplify (a+b)^3+(a-b)^3​

Answer 1

Answer:

2b(3a2+b2)

Step-by-step explanation:

(a+b)3−(a−b)3=(a3+3a2b+3ab2+b3)−(a3−3a2b+3ab2−b3) =6a2b+2b3  =2b(3a2+b2)

If you are allowed complex coefficients this can be broken down into linear factors:

=2b(√3a+ib)(√3a−ib)

Notice also that: (a+b)3+(a−b)3=(b+a)3−(b−a)3=2a(3b2+a2)

there u go please mark me brainalist

Answer 2

Answer:

(a−b)3=a3−3a2b+3ab2−b3  

You can verify this via the binomial expansion theorem or just expanding it:

(a−b)3  

=(a−b)(a−b)(a−b)  

=(a2−2ab+b2)(a−b)  

=a2(a−b)−2ab(a−b)+b2(a−b)  

=a3−a2b−2a2b+2ab2+ab2−b3  

=a3−3a2b+3ab2−b3