Question

$\frac{1}{2}(a+b)(a^2+b^2)+\frac{1}{2}(a-b)(a^2-b^2)$ is equal to

• A. $a^3-b^3$
• B. $a^3+3a^{2}b+3a{b}^2+b^3$
• C. $a^3+b^3$
• D. $a^3-3ab(a+b)-b^3$

Answer 1

The correct option is C $a^3+b^3$

$\Rightarrow \frac{1}{2}(a+b)(a^2+b^2)+\frac{1}{2}(a-b)(a^2-b^2)$
$\Rightarrow \frac{1}{2}(a^3+a^{2}b+a{b}^2+b^3)+\frac{1}{2}(a^3-a^{2}b-a{b}^2+b^3)$
$\Rightarrow \frac{1}{2}(a^3+b^3)+\frac{1}{2}(a^3+b^3)\Rightarrow a^3+b^3$