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

1 Answer
Jul 28, 2018

Answer:

#(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#