# Video: Changing the Subject of a Formula

The variables π and π are related by the formula π(π + 5) = π(π β 19π). Make π the subject.

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### Video Transcript

The variables π and π are related by the formula π multiplied by π plus five is equal to π multiplied by π minus 19π. Make π the subject.

In order to make a variable, in this case π, the subject of a formula, we need to rearrange the formula so that that variable is on its own on one side. As there are πs on both sides of the equation to begin with, we start by distributing the parentheses. On the left-hand side, we multiply π by π and then π by five. This gives us ππ plus five π. We repeat this process on the right-hand side. When distributing the parentheses here, we multiply π by π and π by negative 19π. This gives us ππ minus 19ππ.

Two of our four terms contain a π, ππ and ππ. We need to get these two terms on one side of the equation and the other two terms on the other side. We can do this by adding 19ππ and subtracting ππ from both sides of the equation. On the left-hand side, the ππs cancel and weβre left with five π plus 19ππ. On the right-hand side, we have ππ minus ππ. In order to make π the subject, we next have to factor or factorise the right-hand side. As π is common in both terms, we can factor this out of the parentheses.

ππ divided by π is equal to π and negative ππ divided by π is negative π. Therefore, we have π minus π inside the parentheses. On the left-hand side, we still have five π plus 19ππ. Our final step is to divide both sides by π minus π. On the left-hand side, weβre left with five π plus 19ππ divided by π minus π. On the right-hand side, weβre left with π. Rearranging the formula to make π the subject gives us five π plus 19ππ divided by π minus π.