How do you rearrange a mathematics equation such as 2pr plus 6qs-3qr-4ps?

Answer 1

This is an expression, not an equation.

To rearrange it, you arrange the expression so that the first set of terms have a variable (letter) in common. Arrange the rest so that they follow a similar patter (see working below). Then factorise.

2pr + 6qs - 3qr - 4ps.

Select r to be the common variable for the first two terms.

So 2pr - 3qr + 6qs - 4ps

You will see that terms (now numbered) 3 and 4 have s in common. But, while with the first two, the term with p comes before the term with q, with 3 and 4, it is the other way around. So swap terms 3 and 4.

2pr - 3qr - 4ps + 6qs

Common factor of terms 1 and 2 = r, common factor of terms 3 and 4 = s:

r(2p - 3q) - 2s(2p - 3q)

and then (2p - 3q) is a common factor

so (2p - 3q)(r - 2s)