How do you factor #27 - 125x^3?

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How do you factor #27 - 125x^3?

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Answer 1 · 2016-02-22T21:23:08

$(3 - 5 x) (9 + 15 x + 25 x^{2})$ $(3 - 5x)(9 +15x +25x^2)$

Explanation:

This is a $difference of 2 cubes$ $color(blue) " difference of 2 cubes "$

$27 - 125 x^{3} = 3^{3} - {(5 x)}^{3}$ $27- 125x^3 = 3^3 - (5x)^3$

To factor : $a^{3} - b^{3} = (a - b) (a^{2} + a b + b^{2})$ $a^3 - b^3 = (a - b )(a^2 + ab + b^2)$

For this question let a = 3 and b = 5x

$\Rightarrow 27 - 125 x^{3} = (3 - 5 x) (3^{2} + (3 \times 5 x) + {(5 x)}^{2})$ $rArr 27-125x^3 = (3-5x)(3^2+ (3xx5x) + (5x)^2 )$

$= (3 - 5 x) (9 + 15 x + 25 x^{2})$ $= (3 - 5x )(9 + 15x + 25x^2)$

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How do you factor #27 - 125x^3?

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