Question

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

Answer 1

`8x^3-88x^2+330x-424`

Explanation:

First find `(2x-7)^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).

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

Now for `(2x-9)^2`:
`(2x-9)(2x-9)=4x^2-18x-18x+81`
`=4x^2-36x+81`

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

Not so bad, right? Hope this helps!