# Rearranging Formulae

This section covers using and rearranging formulae and substituting numerical values in formulae.

**To rearrange formulae you should remember the following rules:**

Begin by removing any square roots on both sides of the equation.

Then multiply out any brackets.

Multiply out all terms by the denominator to remove any fractions.

Then Rearrange by collecting the letter you want on one side and everything else on the other. Remember that every term has its own sign in front of it. Negative terms need to be added to both sides to eliminate them.

Factorise the side of the equation your variable is on so there is only one of it.

Then finally divide both sides by whatever the variable is multiplied by.

**Here are some examples:**

2a – b = c

2a= c + b All the terms excluding a are put on the other side of the equation, remember when its move – b becomes + b.

A = __c + b__ Divide through by 2.

2

For the next example we going to make** x** the subject of the equation.

__2 – 3x__ = y

4x + 1 If the subject appears twice in the equation you are likely to need to factorise once all the terms are on one side of the equation.

2 – 3x = y (4x + 1) Then clear the fraction.

2 – 3x = 4xy + y Then multiply out the brackets.

2 = 3x + 4xy + y Then collect all the x terms on one side.

2 – y = 3x + 4xy Put all the terms not including x on one side.

2 – y = x (3+4y) Factorise the terms involving x.

X = __2 – y__ Divide through 3 + 4y.

3+4y

Now let’s make **x** the subject of next equation.

a + b = √10x + y

(a + b)² = 10x + y Square both sides to clear the square root sign.

(a + b)² -y = 10x Put all the terms not including x on one side.

__(a + b)____² - y__ = x Divide through by 10.

10

**Substituting numerical values in formulae**

It is essential to substitute numbers into a given formula accurately.

For example If a = 3b find a when b = 5.

a = 3 x 5² = 3 x 25 = 75 a is not (3 x 5)² you only square the 5.

Another example if b² = c² + 2as find b when c = 5, a = 3 and s =2.

b² = 5² + 2 x -3 x 2 = 25 – 12 = 13

So b = √13 = 3.61 (to 2 decimal places).

The video below explain how to factorise.