Question

Use the binomial Theorem to expand the binomial
(d-4b)^3

Answer 1

what trouble are you having on the binomial theorem?

Answer 2

I honestly don't understand how to do it period. If you could explain it with an example that'd be great.

Answer 3

\[(x+y)^n=\sum_{k=0}^n \left(\begin{matrix}n \\ k\end{matrix}\right)x^{n-k}y^{k} \\ \text{ is the binomial theorem }\]

Answer 4

it is a formula you plug into
you have x is d in this case
and that -4b is y
and that n is 3

Answer 5

If you aren't familiar with that sum notation
then you can write it as
\[(x+y)^n=\left(\begin{matrix}n \\ 0\end{matrix}\right) x^ny^0+\left(\begin{matrix}n \\ 1\end{matrix}\right)x^{n-1} y^1 +\left(\begin{matrix}n \\ 2\end{matrix}\right)x^{n-2}y^2+ \cdots + \left(\begin{matrix}n \\ k\end{matrix}\right) x^{n-k} x^{k} +\cdots \\ +\left(\begin{matrix}n \\ n\end{matrix}\right) x^{0}y^n\]

Answer 6

Examples:
\[(x+1)^2=\left(\begin{matrix}2 \\ 0\end{matrix}\right) x^21^0+\left(\begin{matrix}2 \\ 1\end{matrix}\right) x^1 1^1+\left(\begin{matrix}2 \\ 2\end{matrix}\right) x^01^2 \\ \text{ or after simplifying you should this as } x^2+2x+1\]


\[(x+1)^4=\left(\begin{matrix}4 \\ 0\end{matrix}\right)x^41^0+\left(\begin{matrix}4 \\ 1\end{matrix}\right)x^31^1+\left(\begin{matrix}4 \\ 2\end{matrix}\right)x^21^2+\left(\begin{matrix}4 \\ 3\end{matrix}\right)x^11^3+\left(\begin{matrix}4 \\ 4\end{matrix}\right)x^01^4\]

Answer 7

this is two examples notice the top numbers in the ( ) thingy is staying the same
and the bottom number starting at 0 is moving up 1 integer each time
also notice that the powers of the first term are decreasing while the powers of the second term is increasing until we we reach the powers that are decreasing is 0 and the powers that increase are 4
for that last example


you notice similar things happening in the first example

Answer 8

can you expand this...
\[(f+g)^3=....\]

Answer 9

To freckles and @baby.girl24 :

The following may be helpful as reference material, especially since it ties the Binomial Theorem to Pascal's Triangle.

@baby.girl24: freckles' presentation of the Binomial Theorem is appropriate and correct. However, we need to check whether you have already encountered symbols such as \[\left(\begin{matrix}n \\k\end{matrix}\right)\]

Answer 10

could you share with us what it is that you already understand and what you don't?

Answer 11

Have you seen and used Pascal's Triangle before?

Answer 12

@baby.girl24 : freckles and I have put in significant time towards helping you with your question. Common courtesy suggests that you respond at least enough to ackknowledge any help you receive and inform us when you're moving on to something else.