The correct option is C (x^2+3)(x^4 4x^2+9)^2 x^6+27=(x^2)3+3^3 This is of the form #160; a^3+b^3=(a+b)(a^2 #8722;ab+b^2) . Therefore, ( ...

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Factorization of Expressions Reducible to Difference of Two Squares

Factorize x...

Question

Factorize $x^{6} + 27$ _______________.

(x^{2} + 3) (x^{2} + 3 x + 3) (x^{2} - 3 x + 3)

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(x^{2} - 3) (x^{2} + 3 x + 3) (x^{2} + 3 x + 3)

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(x^{2} + 3) (x^{4} - 4 x^{2} + 9)^{2}

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(x^{2} + 3) (x^{2} - 3 x + 3) (x^{2} - 3 x - 3)

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Solution

The correct option is C $(x^{2} + 3) (x^{4} - 4 x^{2} + 9)^{2}$
$x^{6} + 27 = (x^{2}) 3 + 3^{3}$

This is of the form $a^{3} + b^{3} = (a + b) (a^{2} - a b + b^{2}) .$

Therefore,
$(x^{2})^{3} + 3^{3} = (x^{2} + 3) (x^{4} - 3 x^{2} + 9)$

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