Question

Help

Answer 1

How do you simplify\[\large \frac{ 1 }{ 2 }(2x+5)^9-\frac{ 5 }{ 2 }(2x+5)^8\]and turn it into\[\large x(2x+5)^8\]

Answer 2

still need help

Answer 3

x(2x+5)8 is right :)
^

Answer 4

I know that, but I want to know how to get that result from simplification.

Answer 5

\[\large \frac12(2x+5)^9-\frac52(2x+5)^8\]Rewrite the expression like this if it helps,\[\large \frac12(2x+5)^8(2x+5)-\frac12\cdot5(2x+5)^8\]

Answer 6

From there, we can factor out of each, stuff that they have in common.

Answer 7

\[\large \color{indianred}{\frac12(2x+5)^8}(2x+5)-\color{indianred}{\frac12}\cdot5\color{indianred}{(2x+5)^8}\]Which it turns out is this stuff in red, right?

Answer 8

Maybe artificially put brackets on the outside,
just so you know where the factored stuff will go,\[\large \left[\color{indianred}{\frac12(2x+5)^8}(2x+5)-\color{indianred}{\frac12}\cdot5\color{indianred}{(2x+5)^8}\right]\]factoring,\[\large \color{indianred}{\frac12(2x+5)^8}\left[\qquad\qquad(2x+5)-\quad5\qquad\qquad\right]\]

Answer 9

I left space to show where all the things came from.
Hopefully that's not too confusing.\[\large\rm \frac12(2x+5)^8[2x+5-5]\]And then it's pretty straight forward from there, ya?

Answer 10

Ah ha, thank you zepdrix!