How do you factor $40 v^{3} - 625$ $40v^3-625$ ?

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How do you factor $40 v^{3} - 625$ $40v^3-625$ ?

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Answer 1 · 2015-06-02T17:08:16

$40 = 5 \cdot 8$ $40=5*8$
and $625 = 5 \cdot 125$ $625=5*125$
So $40 v^{3} - 625 = 5 \cdot (8 v^{3}) + 5 \cdot (- 125)$ $40v^3-625=5*(8v^3)+5*(-125)$
$40 v^{3} - 625 = 5 (8 v^{3} - 125)$ $40v^3-625=5(8v^3-125)$

Answer 2 · 2015-06-02T20:39:59

$40 v^{3} - 625$ $40v^3-625$

$= 5 (8 v^{3} - 125)$ $=5(8v^3-125)$

$= 5 ({(2 v)}^{3} - 5^{3})$ $=5((2v)^3-5^3)$

$= 5 ((2 v) - 5) ({(2 v)}^{2} + (2 v) 5 + 5^{2})$ $=5((2v)-5)((2v)^2+(2v)5+5^2)$

$= 5 (2 v - 5) (4 v^{2} + 10 v + 25)$ $=5(2v-5)(4v^2+10v+25)$

...using the difference of cubes identity:

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

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How do you factor $40 v^{3} - 625$ $40v^3-625$ ?

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