# What is the standard form of  y= (2x-7)^3-(2x-9)^2?

Apr 19, 2018

$8 {x}^{3} - 88 {x}^{2} + 330 x - 424$

#### Explanation:

First find ${\left(2 x - 7\right)}^{3}$ and put that in standard form.
Standard form just means that the highest degree term (the variable with the biggest exponent) is first, and they continue in descending order. So ${x}^{5}$ should come before ${x}^{4}$, and the last term is often a constant (a number with no variable attached).

$\left(2 x - 7\right) \left(2 x - 7\right) \left(2 x - 7\right)$
$= \left(4 {x}^{2} - 14 x - 14 x + 49\right) \left(2 x - 7\right)$
$= \left(4 {x}^{2} - 28 x + 49\right) \left(2 x - 7\right)$
$= 8 {x}^{3} - 56 {x}^{2} + 98 x - 28 {x}^{2} + 196 x - 343$
$= 8 {x}^{3} - 84 {x}^{2} + 294 x - 343$
That's the first part in standard form!

Now for ${\left(2 x - 9\right)}^{2}$:
$\left(2 x - 9\right) \left(2 x - 9\right) = 4 {x}^{2} - 18 x - 18 x + 81$
$= 4 {x}^{2} - 36 x + 81$

We've got both parts, so let's subtract:
$8 {x}^{3} - 84 {x}^{2} + 294 x - 343 - \left(4 {x}^{2} - 36 x + 81\right)$
Now just combine like terms, and don't forget to change the signs of the terms in the expression that is being subtracted:
$8 {x}^{3} - 88 {x}^{2} + 330 x - 424$

Not so bad, right? Hope this helps!