(x + y)^3 - (x - y)^3 can be factorized as:

MCQ

$(x + y)^3 - (x - y)^3$ can be factorized as:

A
$2y(3x^2 + y^2)$
✓
$2x(3x^2 + y^2)$
C
$2y(3y^2 + x^2)$
D
$2x(x^2+ 3y^2)$

✓

Answer

Correct option: B.

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

We know the identity
$a^3 - b^3 = (a - b)(a^2 + b^2 + ab)$
Let $x + y = a$ and $x - y = b$
Then,
$a^3 - b^3$
$= (x + y)^3 - (x - y)^3$
$= [(x + y) - (x - y)][(x + y)^2 + (x - y)^2 + (x + y)(x - y)]$
$= 2y[x^2 + y^2 + 2xy + x^2 + y^2 - 2xy + x^2 - y^2]$
$= 2y(3x^2 + y^2)$

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

More "M.C.Q" from Factorization Of Algebraic Expressions→Factorization Of Algebraic Expressions — all question types→MATHS STD 9 question papers→Rajasthan Board STD 9 question papers→Rajasthan Board question paper generator→

Factorization Of Algebraic Expressions — MATHS STD 9 — Question

Answer

Need a full question paper?

Explore more

Similar questions