Question

Factorise the following:

ab(x² + y²) – xy(a² + b²)

Answer 1

Given: ab(x² + y²) – xy(a² + b²)

Step-wise calculation:

1. Expand and rearrange: abx² + aby² – a²xy – b²xy.

2. Rewrite grouping terms cleverly: abx² – b²xy + aby² – a²xy.

3. Group terms in two pairs: x(abx – b²y) + y(aby – a²x).

4. Rearrange inside the parentheses: xb(ax – by) + ya(by – ax).

5. Note that: by – ax = –(ax – by).

6. So: xb(ax – by) + ya(– (ax – by)) = (ax – by)(xb – ya).

7. Since: xb – ya = –(ax – by) the expression is (ax – by)(bx – ay).