Question

Expand (x-y)^4 using the fourth terms in the binomial expansion



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Answer 1

`~\hfill \textit{Binomial Theorem Expansion}~\hfill \\\\ {\Large \begin{array}{llll} (x-y)^(4) \end{array}}~\hspace{4em} \begin{array}{cccl} term&coefficient&value\\ \cline{1-3}&\\ 1 & 1 & (x)^(4)~(-y)^(0)\\ 2 & 4 & (x)^(3)~(-y)^(1)\\ 3 & 6 & (x)^(2)~(-y)^(2)\\ 4 & 4 & (x)^(1)~(-y)^(3)\\ 5 & 1 & (x)^(0)~(-y)^(4)\\ \end{array} \\\\[-0.35em] ~\dotfill\\\\ ~\hfill {\Large \begin{array}{llll} x^4-4x^3y+6x^2y^2-4xy^3+y^4 \end{array}}~\hfill`

if you ever wonder how to get the coefficient sequentially, the way I do it is by multiplying the current coefficient times the exponent of the first term divided by the exponent of the second term+1, now that's a bit of a mouthful.

so say how did we get 6 for the next coefficient?

4*3÷2

how did we get 4 for the next one from 6x²y²?

6*2÷3

and so on.