How do you factor $- 375 a^{3} + 648$ $-375a^3 + 648$ ?

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Answer 1 · 2015-09-25T15:51:06

$3 (6 - 5 a) (36 + 30 a + 25 a^{2})$ $3(6-5a)(36+30a +25a^2)$

To factorise, we can try to put into the shape of difference of cubes, to see if this can help. Accordingly,

$- 375 a^{3} + 648 = 3 (216 - 125 a^{3})$ $-375a^3 +648 = 3( 216- 125a^3)$

= $3 (6^{3} - 5^{3} a^{3})$ $3(6^3 - 5^3 a^3)$

= $3 (6 - 5 a) (6^{2} + 6 \cdot 5 a + 5^{2} a^{2})$ $3(6-5a)(6^2 +6*5a +5^2a^2)$

= $3 (6 - 5 a) (36 + 30 a + 25 a^{2})$ $3(6-5a)(36+30a +25a^2)$

How do you factor -375a^3 + 648−375a3+648-375a^3 + 648?