How do you simplify (w+2t)(w^2-2wt+4t^2)?

1 Answer
Jul 28, 2018

(w+2t)(w^2-2wt+4t^2) = w^3+8t^3

Explanation:

The given expression is in the form:

(A+B)(A^2-AB+B^2)

with A=w and B=2t.

This is recognisable as the factored form (using real coefficients) of the sum of cubes:

A^3+B^3 = (A+B)(A^2-AB+B^2)

If you wanted to multiply it out by hand, you could use distributivity as follows:

(w+2t)(w^2-2wt+4t^2) = w(w^2-2wt+4t^2)+2t(w^2-2wt+4t^2)

color(white)((w+2t)(w^2-2wt+4t^2)) = w^3-color(red)(cancel(color(black)(2w^2t)))+color(green)(cancel(color(black)(4wt^2)))+color(red)(cancel(color(black)(2w^2t)))-color(green)(cancel(color(black)(4wt^2)))+8t^3

color(white)((w+2t)(w^2-2wt+4t^2)) = w^3+8t^3