Simplify the factor completely: $4 (x^{3} + 1) (x^{2} - 9)$

4 (x + 1) (x^{2} - x + 1) (x + 3) (x + 3)

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4 (x + 1) (x^{2} - x + 1) (x - 3) (x + 3)

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4 (x + 1) (x^{2} - x + 1) (x + 3)^{2}

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(x - 1) (x^{2} - x + 1) (x - 3) (x + 3)

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Solution

The correct option is B $4 (x + 1) (x^{2} - x + 1) (x - 3) (x + 3)$
$4 (x^{3} + 1) (x^{2} - 9)$
We know that $x^{3} + y^{3} = (x + y) (x^{2} - x + 1)$
$x^{2} - y^{2} = (x - y) (x + y)$
So, $4 (x^{3} + 1) (x^{2} - 3^{2}) = 4 (x + 1) (x^{2} - x + 1) (x - 3) (x + 3)$

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(i) $(x + 1) (x - 1) (x^{2} + 1)$
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Simplify the factor completely: 4(x3+1)(x2−9)

The correct option is B 4(x+1)(x2−x+1)(x−3)(x+3)4(x3+1)(x2−9)We know that x3+y3=(x+y)(x2−x+1)x2−y2=(x−y)(x+y)So, 4(x3+1)(x2−32)=4(x+1)(x2−x+1)(x−3)(x+3)

Simplify the factor completely: $4 (x^{3} + 1) (x^{2} - 9)$

The correct option is B $4 (x + 1) (x^{2} - x + 1) (x - 3) (x + 3)$
$4 (x^{3} + 1) (x^{2} - 9)$
We know that $x^{3} + y^{3} = (x + y) (x^{2} - x + 1)$
$x^{2} - y^{2} = (x - y) (x + y)$
So, $4 (x^{3} + 1) (x^{2} - 3^{2}) = 4 (x + 1) (x^{2} - x + 1) (x - 3) (x + 3)$