# Thread: Expanding and subtracting binomials

1. ## Expanding and subtracting binomials

I'm working on expanding binomials and I currently understand how to expand basic ones using the binomial theorem. But due to transferring to my Precalc class late, I missed the lecture on them. Could someone explain how to expand and simplify this expression using the binomial theorem?

$\displaystyle 2(x-3)^4 + 5(x-3)^2$

2. ## Re: Expanding and subtracting binomials

Originally Posted by zsf1990
I'm working on expanding binomials and I currently understand how to expand basic ones using the binomial theorem. But due to transferring to my Precalc class late, I missed the lecture on them. Could someone explain how to expand and simplify this expression using the binomial theorem?

$\displaystyle 2(x-3)^4 + 5(x-3)^2$

OH, Come on!
$\displaystyle 2(x-3)^4 + 5(x-3)^2=(x-3)^2[2(x-3)^2+5][$

3. ## Re: Expanding and subtracting binomials

I don't think I understand what you mean. The book gives $\displaystyle 2x^4-24x^3+113x^2-246x+207$ as the solution. I got $\displaystyle 2x^4 - 8x^3 3 + 17x^2 9 - 14x27 + 126$ by applying the 2 and 5 after expanding, then combining like terms. I'm not sure where I messed up.

4. ## Re: Expanding and subtracting binomials

Originally Posted by zsf1990
I don't think I understand what you mean. The book gives $\displaystyle 2x^4-24x^3+113x^2-246x+207$ as the solution. I got $\displaystyle 2x^4 - 8x^3 3 + 17x^2 9 - 14x27 + 126$ by applying the 2 and 5 after expanding, then combining like terms. I'm not sure where I messed up.

5. ## Re: Expanding and subtracting binomials

Knowing the answer does me no good if I don't know how to get there. I know how to expand the binomial $\displaystyle (x - 3)^4$ and how to subtract the two expanded terms. What I don't understand is what to do with the 2 and the 5.

6. ## Re: Expanding and subtracting binomials

Originally Posted by zsf1990
Knowing the answer does me no good if I don't know how to get there. I know how to expand the binomial $\displaystyle (x - 3)^4$ and how to subtract the two expanded terms. What I don't understand is what to do with the 2 and the 5.
Once you expand each of the terms using the Binomial Theorem, multiply each term through by 2 or 5 (depending on which number is out the front).

However, Plato's advice gives you an easier alternative form to work with.