Question

Mark the correct alternative in each of the following: $(x+y{)}^3-(x-y{)}^3$ can be factorized as

• A. $2x(x^2+3y^2)$
• B. $2x(3x^2+y^2)$
• C. $2y(3x^2+y^2)$
• D. $2y(3y^2+x^2)$

Answer 1

The correct option is C $2y(3x^2+y^2)$

Given: $(x+y{)}^3-(x-y{)}^3$

$\therefore (x+y{)}^3-(x-y{)}^3$

$=\left[\right(x+y)-(x-y\left)\right]\left[\right(x+y{)}^2+(x+y)(x-y)+(x-y{)}^2]$

$[\because a^3-b^3=(a-b\left)\right(a^2+ab+b^2\left)\right]$

$=(x+y-x+y)(x^2+2xy+y^2+x^2-y^2+x^2-2xy+y^2)$

$=2y(3x^2+y^2)$

Hence, option $\left(A\right)$ is the correct answer.