# Expanding and subtracting binomials

• Jan 20th 2013, 05:01 PM
zsf1990
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\$

• Jan 20th 2013, 05:30 PM
Plato
Re: Expanding and subtracting binomials
Quote:

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][\$
• Jan 20th 2013, 05:36 PM
zsf1990
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.
• Jan 20th 2013, 05:48 PM
Plato
Re: Expanding and subtracting binomials
Quote:

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.

• Jan 20th 2013, 06:10 PM
zsf1990
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.
• Jan 20th 2013, 07:29 PM
Prove It
Re: Expanding and subtracting binomials
Quote:

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.