Question

Factor Sums and Differences of Cubes 125-27w^3

Answer 1

Given

`125-27w^3`

Recall that

`(a^3-b^3)=(a-b)(a^2+ab+b^2)`

Therefore,

`\begin{gathered} 125-27w^3=(5)^3-(3w)^3 \\ \\ \textet a=5,b=3w \\ \\ \Rightarrow(5)^3-(3w)^3=(5-3w)((5)^2+(5)(3w)+(3w)^2) \\ \\ =(5-3w)(25+15w+9w^2) \end{gathered}`