### 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 πs 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 ππ 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 ππ minus 19ππ.

Two of our four terms contain a π, ππ and ππ. 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 19ππ and subtracting ππ from both sides of the equation. On the left-hand side, the ππs cancel and weβre left with five π plus 19ππ. On the right-hand side, we have ππ minus ππ. 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.

ππ divided by π is equal to π and negative ππ 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 19ππ. Our final step is to divide both sides by π minus π. On the left-hand side, weβre left with five π plus 19ππ divided by π minus π. On the right-hand side, weβre left with π. Rearranging the formula to make π the subject gives us five π plus 19ππ divided by π minus π.