Sum and Difference of Cubes

Question

Factor Each Expression:

375x³−192 =

Answer 1

375x^3 - 192

= 3(125x^3 - 64)

=3((5x)^3 - 4^3)

= 3(5x-4)(25x^2 +20x + 16)

using the general formula a^3-b^3 = (a-b)(a^2 +ab +b^2)

where a= 5x, b = 4

Answer 2

375x³ − 192 = 3(125x³ − 64)

a³ – b³ = (a – b)(a² + ab + b²)

Applying this factoring the expression above

a³ = 125x³ and b³ = 64

a² = 25x² and b² = 16

a = 5x and b =4

So the factored expression is

375x³ − 192 = 3(5x – 4)(25x² + 20x + 16)