Question

Simplify:

${(x+y)}^3+{(x-y)}^3+6x(x^2-y^2)$

• A. $8x^3$
• B. $6x^3$
• C. $6x^2$
• D. $8x^2$

Answer 1

The correct option is A $8x^3$

Let $(x+y)=a$ and $(x-y)=b$
Then, ${(x+y)}^3+{(x-y)}^3+6x(x^2-y^2)={(x+y)}^3+{(x-y)}^3+3\times 2x\times (x+y)(x-y)$
$={(x+y)}^3+{(x-y)}^3-3\times \left[\right(x+y\left)\right(x-y\left)\right]\times (x+y)(x-y)$
$=a^3+b^3+3ab(a+b)={(a+b)}^3$
$={(x+y+x-y)}^2={\left(2x\right)}^3={8x}^3$