Question

Expand (x+y)^3.

Answer 1

x^3 + y^3

Answer 2

\[\left(\begin{matrix}3 \\ 0\end{matrix}\right)\]

Answer 3

I know how to solve it using that method. But I need to use a different method to solve this problem. \[\left(\begin{matrix}3 \\ 0\end{matrix}\right)x^0y^3+\left(\begin{matrix}3 \\ 1\end{matrix}\right)x^1y^2+\left(\begin{matrix}3 \\ 2\end{matrix}\right)x^2y+\left(\begin{matrix}3 \\ 3\end{matrix}\right)x^3y^0=y^3+3xy^2+3x^2y+x^3\]

Answer 4

And I don't know how to evaluate the matrices above.

Answer 5

what matrices?

Answer 6

The matrices (3, 0), (3, 1), and (3, 2), (3, 3).

Answer 7

those aren't matrices

Answer 8

\[{n\choose k}=\frac{n!}{k!(n-k)!}\]

Answer 9

\[{3\choose 1}=\frac{3!}{1!(3-1)!}=\frac{3\times 2\times1}{1\times2\times 1}=3\]

Answer 10

You were right! Thanks!