Simplify: (x + y)^3 + (x - y)^3 +6x (x^2 - y^2) - Vidyadip

MCQ

Simplify: $(x + y)^3 + (x - y)^3 +6x (x^2 - y^2)$

✓
$8x^3$
B
$6x^3$
C
$6x^2$
D
$8x^2$

✓

Answer

Correct option: A.

$8x^3$

Given, $(x + y)^3+ (x - y)^3 +6x (x2 - y2)$
$\because$ $(x + y)^3 = x^3 + y^3 + 3xy (x + y)$
$\because$ $(x - y)^3 = x^3 - y^3- 3xy (x - y)$
$⇒ x^3+ y^3 + 3xy (x + y) + x^3 - y^3 - 3xy (x - y) + 6x (x^2 − y^2)$
$⇒ x^3 + y^3 + 3x^2y + 3xy^2 + x^3 - y^3 - 3x^2y + 3xy^2 + 6x^3 - 6xy^2$
$⇒ 8x^3$

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