MCQ
$(x + y)^3 - (x - y)^3$ can be factorized as:
- A$2x(3x^2 + y^2)$
- B$2y(3y^2 + x^2)$
- ✓$2y(3x^2 + y^2)$
- D$2x(x^2 + 3y^2)$
✓
Answer
Correct option: C.
$2y(3x^2 + y^2)$
Put $a = x + y$ and $b = x - y, $ then
$(x+y)^3-(x-y)^3=a^3-b^3$
$=(a-b)\left(a^2+b^2+a b\right)$
$=(x+y-x+y)\left[(x+y)^2+(x-y)^2+(x-y)(x+y)\right]$
$=2 y\left[2\left(x^2+y^2\right)+\left(x^2-y^2\right)\right]$
$=2 y\left[3 x^2+y^2\right]$
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