# Thread: steps to simplify a problem

1. ## steps to simplify a problem

Hello, can someone show me the steps to simplifying:
$\displaystyle \Delta y=(t+\Delta t)^2 - t^2 + 8(t+\Delta t)-8t$
to
$\displaystyle \Delta y=2t(\Delta t)$$\displaystyle +(\Delta t)^2$$\displaystyle +8$$\displaystyle \Delta$$\displaystyle t$

2. Hi there integral, all you need to do here is expand the expression and group the like terms.

3. $\displaystyle \Delta y=(t+\Delta t)^2 -t^2 +8(t+\Delta t)-8t$
$\displaystyle \Delta y=(t+\Delta t)(t+\Delta t) -t^2 +8(t+\Delta t)-8t$
$\displaystyle \Delta y=t^2+t\Delta t+ (\Delta t(t))+\Delta t^2 -t^2 +8(t+\Delta t)-8t$
$\displaystyle \Delta y=t^2+t\Delta t+ (\Delta t(t))+\Delta t^2 -t^2 +8\Delta t$
$\displaystyle \Delta y=t\Delta t+ t\Delta t+\Delta t^2 +8\Delta t$
$\displaystyle \Delta y=2(t\Delta t)+\Delta t^2 +8\Delta t$

right? I feel so dumb now. lol

4. Looks ok, I would do it like this.

$\displaystyle \Delta y=(t+\Delta t)^2 - t^2 + 8(t+\Delta t)-8t$

Grouping

$\displaystyle \Delta y=[(t+\Delta t)^2 - t^2] + [8(t+\Delta t)-8t]$

Using the difference of 2 squares in the first part and expanding the 2nd part we get

$\displaystyle \Delta y=((t+\Delta t) - t)((t+\Delta t)+ t) + [8t+8\Delta t)-8t]$

And simplifying

$\displaystyle \Delta y=\Delta t (2t+\Delta t) + 8\Delta t$

And expanding again

$\displaystyle \Delta y=2t(\Delta t)+(\Delta t)^2 + 8\Delta t$

5. That works as well (Thanks for the idea).
Thank you