Question

How do you factor 54-16x^3? The answer is 2(3-2x)(9+6x+4x^2), but I don't know how to get there.

Answer 1

You will need the identity

(A³-B&sup3)=(A-B)(A²+AB+B²)

54-16x^3
=2(27-8x³)
=2(3³-(2x)³)
=2(3-2x)(3²+3*2x+(2x)²)
=2(3-2x)(9+6x+4x²)