How do you factor $125 x^{3} - 27$ $125x^3-27$ ?

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How do you factor $125 x^{3} - 27$ $125x^3-27$ ?

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Answer 1 · 2018-05-09T12:32:04

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

Explanation:

$125 x^{3} - 27 is a difference of cubes$ $125x^3-27" is a "color(blue)"difference of cubes"$

$and factors in general as$ $"and factors in general as"$

$∙ x a^{3} - b^{3} = (a - b) (a^{2} + a b + b^{2})$ $•color(white)(x)a^3-b^3=(a-b)(a^2+ab+b^2)$

$125 x^{3} = {(5 x)}^{3} \Rightarrow a = 5 x$ $125x^3=(5x)^3rArra=5x$

$27 = {(3)}^{3} \Rightarrow b = 3$ $27=(3)^3rArrb=3$

$\Rightarrow 125 x^{3} - 27 = (5 x - 3) ({(5 x)}^{2} + (5 x \times 3) + 3^{2})$ $rArr125x^3-27=(5x-3)((5x)^2+(5x xx3)+3^2)$

$\times \times \times \times \times = (5 x - 3) (25 x^{2} + 15 x + 9)$ $color(white)(xxxxxxxxxx)=(5x-3)(25x^2+15x+9)$

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How do you factor $125 x^{3} - 27$ $125x^3-27$ ?

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