How do you factor $b^{3} + 27$ $b^3 + 27$ ?

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How do you factor $b^{3} + 27$ $b^3 + 27$ ?

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Answer 1 · 2016-02-03T00:23:42

$b^{3} + 27 = (b + 3) (b^{2} - 3 b + 9)$ $b^3+27=(b+3)(b^2-3b+9)$

Explanation:

$b^{3} + 27$ $b^3+27$ is an example of a sum of cubes, where $a = b$ $a=b$ and $b = 3 .$ $b=3.$ . Rewrite the expression as ${(b)}^{3} + {(3)}^{3}$ $(b)^3+(3)^3$ .

To solve the sum of cubes, use the equation $a^{3} + b^{3} = (a + b) (a^{2} - a b + b^{2})$ $a^3+b^3=(a+b)(a^2-ab+b^2)$ .

Substitute the values for $a and b$ $a and b$ into the equation.

${(b)}^{3} + {(3)}^{3} = (b + 3) (b^{2} - (b) (3) + 3^{2})$ $(b)^3+(3)^3=(b+3)(b^2-(b)(3)+3^2)$

Simplify.

${(b)}^{3} + {(3)}^{3} = (b + 3) (b^{2} - 3 b + 9)$ $(b)^3+(3)^3=(b+3)(b^2-3b+9)$

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How do you factor $b^{3} + 27$ $b^3 + 27$ ?

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