Question

Expand the binomial raised to a power. (x-y)^4

Answer 1

The key is to use Pascal's Triangle, or combinations if you are familiar with them

Poorly drawn Pascal's Triangle:
1
1 1
1 2 1
1 3 3 1
1 4 6 4 1
.... etc

This gives the coefficients. Since one term is negative and the other is positive, the sign will alternate. So:
(x-y)^4 = x^4 - 4x^3*y^1 + 6x^2*y^2 - 4x^1*y^3 + y^4

Alternatively, if you use combinations, you can find the coefficients of a term like so:
\[\left(\begin{matrix}4 \\ 0\end{matrix}\right)x^4 - \left(\begin{matrix}4 \\ 1\end{matrix}\right)x^3y^1 + \left(\begin{matrix}4 \\ 2\end{matrix}\right)x^2y^2-\left(\begin{matrix}4 \\ 3\end{matrix}\right)x^1y^3+\left(\begin{matrix}4 \\ 4\end{matrix}\right)xy^4\]

Where
\[\left(\begin{matrix}4 \\ 0\end{matrix}\right) \]
is "4 Choose 0".
That may be beyond what you're familiar with. If so, just use Pascal's Triangle

Answer 2

Typo on that last term, should be y^4 not xy^4

Answer 3

Thanks bro :)