Factorising - Intermediate & Higher tier – WJECChange the subject of a formula with factorising

Factorising is a way of writing an expression as a product of its factors using brackets. We do this by taking out any factors that are common to every term in the expression.

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Changing the subject of a formula involving factorising - Higher tier

Factorising can be used to help us when rearranging formulae. If the term you are making the subject appears more than once, you will need to factorise at some point.

Example one

Make \(\text{x}\) the subject of the formula \(\text{y = wx + w} - \text{5x}\).

Firstly, we need to move any terms not related to \(\text{x}\):

An infographic showing how to move terms not related to x in the equation y = wx + w - 5x to give y - w = wx - 5x.

We now have all the \(\text{x}\) terms together. To make \(\text{x}\) appear only once, we will need to factorise the right hand side of the equation.

The HCF of \(\text{wx}\) and \(\text{5x}\) is \(\text{x}\), so \(\text{x}\) will come outside the bracket.

\(\text{wx ÷ x = w}\)

\(\text{5x ÷ x = 5}\)

So we now have: \(\text{y – w = x(w – 5)}\)

Finally, we need to rearrange the equation by dividing to get \(\text{x}\) on its own:

An infographic showing how to rearrange the equation y - w = x(w-5), by dividing to get x on its own and give x = y - w divided by w - 5.

We usually place the subject of a formula on the left hand side, so the equation becomes:

An infographic showing the equation x = y - w divided by w - 5.

Example two

Make \(\text{x}\) the subject of the formula \(\text{y} = \frac{4x + 5}{x}\)

An infographic showing how to make x the subject of the formula y = 4x - 5 divided by x to give x = 5 divided by y - 4.

Question

Make \(\text{x}\) the subject of the formula \(\text{ax + b = cx + d}\)

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