Question

Solve: $(a+b{)}^3-(a-b{)}^3$.

• A. $2a(3a^2+b^2)$
• B. $2b(3a^2+b^2)$
• C. $2(a^3+b^3)$
• D. None

Answer 1

The correct option is B $2b(3a^2+b^2)$

We know, $(a+b{)}^3=a^3+b^3+3a^{2}b+3a{b}^2$

$⟹$ $(a+b{)}^3=a^3+b^3+3ab(a+b)$.

Also, $(a-b{)}^3=a^3-b^3-3a^{2}b+3a{b}^2$

$⟹$ $(a-b{)}^3=a^3-b^3-3ab(a-b)$.

Then, $(a+b{)}^3-$ $(a-b{)}^3$

$=a^3+b^3+3a^{2}b+3a{b}^2$ $-(a^3-b^3-3a^{2}b+3a{b}^2)$

$=a^3+b^3+3a^{2}b+3a{b}^2$ $-a^3+b^3+3a^{2}b-3a{b}^2$

$=b^3+3a^{2}b$ $+b^3+3a^{2}b$

$=2b^3+6a^{2}b$

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

Therefore, option $B$ is correct.