How do you simplify (w+2t)(w^2-2wt+4t^2)?
1 Answer
Jul 28, 2018
Explanation:
The given expression is in the form:
(A+B)(A^2-AB+B^2)
with
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