Question

Expand (2x + y)5.

Answer 1

Have you drawn yourself a triangle. It looks like you may need one.

Answer 2

This Is A Binomial Theorem

Answer 3

OH yes. You can use combinations to figure out the coefficients or just keep drawing the triangle. The triangle is quicker until you get to some higher powers.

Answer 4

Is There A Formula For This ?

Answer 5

\[(a+b)^n=\sum_{k=0}^n\begin{pmatrix}n\\k\end{pmatrix}a^{n-k}b^k\]

\[\begin{align}
(a+b)^1&=1(a+b)&&=a+b\\
(a+b)^2&=1a^2b^0+2a^1b^1+1a^0b^2&&=a^2+2ab+b^2\\
(a+b)^3&=1a^3b^0+3a^2b^1+3a^1b^2+a^0b^3&&=a^3+3a^2b+3ab^2+b^3\\
\vdots
\end{align}\]

Answer 6

Are you good with the formula above?

Answer 7

I Think So.... I Just Plug Everything Inside ?

Answer 8

Yes. As long as you have the rows of the triangle on paper it's not a big deal. Just notice the pattern of how the exponents change and be careful when negatives are being raised to powers.

Answer 9

No Im Lost !

Answer 10

Let walk through it. There is a lot to do for a full expansion.

Triangle row ----> 1 5 10 10 5 1 (Good?)