Help simplifying

**el123** · September 11th 2009, 10:49 PM

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?

**running-gag** · September 11th 2009, 11:26 PM

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

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

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

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

**el123** · September 12th 2009, 01:29 AM

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.

**Matt Westwood** · September 12th 2009, 04:51 AM

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:

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

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

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

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