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What will be the factors of $x + 2 3 + x − 2 3$ ?

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(2 x) x 2 − 12

(2 x) x 2 + 12

(2 x) x 2 + 15

(2 x) x 2 + 16

answer is B.

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Detailed Solution

We have to find the factors of

x + 2 3 + x − 2 3

.
Considering the formula of factorization of the sum of two cubes,

x 3 + y 3 = (x + y) x 2 − x y + y 2

Factoring the given expression by applying the formula,

(x + 2) 3 + (x − 2) 3 = {(x + 2) + (x − 2)} (x + 2) 2 − (x + 2) (x − 2) + (x − 2) 2 (x + 2) 3 + (x − 2) 3 = (2 x) x 2 + 4 x + 4 − x 2 − 4 + x 2 − 4 x + 4

Evaluating the obtained equation,

(x + 2) 3 + (x − 2) 3 = (2 x) 2 x 2 + 8 − x 2 + 4 (x + 2) 3 + (x − 2) 3 = (2 x) x 2 + 12

So, the factors of

x + 2 3 + x − 2 3

are

(2 x) x 2 + 12

.
Therefore, option 2 is correct.

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