Question

How do I extract common factors from this equation?

6(2x+5)^2(3x-4)-6(2x+5)^3/(3x-4)3

Answer 1

My coursework shows this... 6(2x+5)^2(3x-4-2x-5)/(3x-4)^3

I just don't understand how they get it??

Answer 2

We have
\[6(2x+5)^2(3x-4)-\frac{6(2x+5)^3}{(3x-4)^3}\]
We can notice the common term (2x+5) in both the terms
\[6\underline{(2x+5)^2}(3x-4)-\frac{6\underline {(2x+5)^3}}{(3x-4)^3}\]
We can take (2x+5)^2 common from both the terms
so we get
\[(2x+5)^2(6(3x-4)-\frac{6(2x+5)}{(3x-4)^3})\]
We can take 6 also common from both the terms, we get
\[6(2x+5)^2((3x-4)-\frac{(2x+5)}{(3x-4)^3})\]

Answer 3

Good explanation. Thank you.