How to factor 16x9 + 54y3 using difference of cubes?

1 Answer
Oct 10, 2017

16x9+54y3=2(2x3+3y)(4x46x3y+9y2)

Explanation:

Here we have sum of cubes and not difference of cubes. Hence, we have to use a3+b3=(a+b)(a2ab+b2). As such

16x9+54y3

= 2(8x9+27y3)

= 2((2x3)3+(3y)3)

= 2((2x3)+(3y))((2x3)2(2x3)(3y)+(3y)2)

= 2(2x3+3y)(4x46x3y+9y2)