How do you factor $16 a x^{3} + 54 a y^{3}$ $16ax^3 + 54ay^3$ ?

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Answer 1 · 2015-06-07T20:55:19

$16 a x^{3} + 54 a y^{3}$ $16ax^3+54ay^3$

$= 2 a (8 x^{3} + 27 y^{3})$ $=2a(8x^3+27y^3)$

$= 2 a ({(2 x)}^{3} + {(3 y)}^{3})$ $=2a((2x)^3+(3y)^3)$

$= 2 a (2 x + 3 y) ({(2 x)}^{2} - (2 x) (3 y) + {(3 y)}^{2})$ $=2a(2x+3y)((2x)^2-(2x)(3y)+(3y)^2)$

$= 2 a (2 x + 3 y) (4 x^{2} - 6 x y + 9 y^{2})$ $=2a(2x+3y)(4x^2-6xy+9y^2)$

...using the sum of cubes identity:

$A^{3} + B^{3} = (A + B) (A^{2} - A B + B^{2})$ $A^3+B^3 = (A+B)(A^2-AB+B^2)$

There are no simpler factors with real coefficients.

How do you factor 16ax3+54ay316ax^3 + 54ay^3?