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

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

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Answer 1 · 2018-07-30T21:43:28

$(5 e - 3 f) (25 e^{2} + 15 e f + 9 f^{2})$ $(5e-3f)(25e^2+15ef+9f^2)$

Explanation:

$this is a difference of cubes$ $"this is a "color(blue)"difference of cubes"$

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

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

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

$= (5 e - 3 f) ({(5 e)}^{2} + 5 e \cdot 3 f + {(3 f)}^{2})$ $=(5e-3f)((5e)^2+5e*3f+(3f)^2)$

$= (5 e - 3 f) (25 e^{2} + 15 e f + 9 f^{2})$ $=(5e-3f)(25e^2+15ef+9f^2)$

Answer 2 · 2018-07-30T21:50:44

$(5 e - 3 f) (25 e^{2} + 15 e f + 9 f^{2})$ $(5e-3f)(25e^2+15ef+9f^2)$

Explanation:

What we have is a difference of cubes, which factors as follows:

$bar(ul|color(white)(2/2)(a^3-b^3)=(a-b)(a^2+ab+b^2)color(white)(2/2)|$

We have the following:

$125e^3-27f^3$ , where $a=root3(125e^3)$ , and $b=root3(27f^3)$ .

Simplifying these, we get $a=5e$ and $b=3f$ . Let's plug these into our difference of cubes expression to get

$(5e-3f)(25e^2+15ef+9f^2)$

Hope this helps!

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

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