Question

plzz answer in steps??​

Answer 1

Answer:

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Expanding:

(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)

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Answer 2

(a+b)^3 - (a-b)^3

= a^3 + b^3 + 3ab(a+b) - [a^3 - b^3 -3ab(a-b)]

= a^3 + b^3 + 3(a^2)b + 3a(b^2) - a^3 + b^3 + 3(a^2)b -3a(b^2)

= 2b^3 + 6(a^2)b

= 2b(b^2 + 3a^2)

So 2b is a factor of (a+b)^3 - (a-b)^3.