1. ## Help simplifying

I can't seem to simplify this correctly

$20(5-\frac{t}{4})-2(5-\frac{t}{4})^2 + t(5-\frac{t}{4})$
Can someone show me step by step how i break this down?

2. Originally Posted by el123
I can't seem to simplify this correctly

$20(5-\frac{t}{4})-2(5-\frac{t}{4})^2 + t(5-\frac{t}{4})$
Can someone show me step by step how i break this down?
Hi

You can see that $5-\frac{t}{4}$ can be factored

$20\left(5-\frac{t}{4}\right)-2\left(5-\frac{t}{4}\right)^2 + t\left(5-\frac{t}{4}\right) = \left(5-\frac{t}{4}\right)\left(20 - 2 \left(5-\frac{t}{4}\right) + t\right)$

$20\left(5-\frac{t}{4}\right)-2\left(5-\frac{t}{4}\right)^2 + t\left(5-\frac{t}{4}\right) = \left(5-\frac{t}{4}\right)\left(20-10+\frac{t}{2}+t\right)$

$20\left(5-\frac{t}{4}\right)-2\left(5-\frac{t}{4}\right)^2 + t\left(5-\frac{t}{4}\right) = \left(5-\frac{t}{4}\right)\left(10+\frac{3t}{2}\right)$

3. ok i orginally wrote it wrong but i get what t6 do , but now im stuck on this part

$-2(5-\frac{t}{4})^2$

I keep getting

$-2(25 -10t+\frac{t^2}{4}$

which gives
$-50 + 20t+\frac{t^2}{8}$

But it doesn't fit into what my answer should be, i think i expanded that wrong.

4. Originally Posted by el123
ok i orginally wrote it wrong but i get what t6 do , but now im stuck on this part

$-2(5-\frac{t}{4})^2$

I keep getting

$-2(25 -10t+\frac{t^2}{4}$

which gives
$-50 + 20t+\frac{t^2}{8}$

But it doesn't fit into what my answer should be, i think i expanded that wrong.
Like this:

$-2\left({5-\frac{t}{4}}\right)^2$

$= -2 \left({5^2 - 2 \times 5 \left({\frac{t}{4}}\right) + \left({\frac{t}{4}}\right)^2}\right)$

$= -2 \left({5^2 - \frac {5t} 2 + \frac{t^2}{16}}\right)$