Expand \((x-y)^6\) by the binomial theorem…

Could we write out the expansion using the binomial formula? (We’ll need to be careful with the signs…)

Would the appropriate line of Pascal’s triangle help?

…and use the result to evaluate \(\left(19\tfrac{3}{4}\right)^6\) correct to the nearest thousand.

Can we choose sensible values for \(x\) and \(y\) such that \(x-y=19\tfrac{3}{4}\), making the calculations of \(x^n\) and \(y^n\) relatively easy?

Since we only need to know the result to the nearest thousand, can we ignore some terms of the expansion?