In this section we are going to look at multiplying and dividing in algebra. Here are a few simple rules to help you get started with multiplying algebra. It is very similar to multiplying numbers.

### Using letters in algebra

#### 👉 abc stands for a × b × c and 3a stands for three times a.

To make it clearer (and quicker to write), it is common to leave out the multiplication x's.

#### 👉 $$\mathrm{nm}^{2}$$ means the same as n × m × m

Please remember that it is only m that is squared.

#### 👉 $$(n m)^{2}$$ means the same as n × n × m × m

Both n and m are squared as they are both inside the brackets.

#### Example

Simplify m × m × m × m × m = $$m^{5}$$
So, we have m multiplied 5 times, $$m^{5}$$

#### Example

Simplify 3m × 6n × 12
It is necessary to multiply the numbers together first, and then the letters will also be multiplied together.
= 3 × 6 × 12 × m × n
= 216mn

#### Example

Simplify $$15 m^{2} \div 20 m$$
To simplify things, we will need to write the division as a fraction.
= $$15 m^{2} \div 20 m$$
= $$\frac{6 m^{2}}{8 m}$$
= $$\frac{3}{4} m$$

### Multiplying brackets

If you multiply brackets, the thing that you need to remember is that the thing outside the brackets multiplies each of the terms inside the brackets.

#### Example

Expand 6(4x + 8)
= (6 × 4x) + (6 × 8)
= 24x + 48

#### Example

Expand x(3x + 2) + y(y - 8) + 6x(y + 4)
To solve this larger equation, we need to deal with it parts. So, we start by expanding each bracket separately.

Expand $$=3 x^{2}+2 x+y^{2}-8 y+6 x y+24 x$$
Group like terms $$=3 x^{2}+24 x+2 x+6 x y+y^{2}-8 y$$
Simplify $$=3 x^{2}+26 x+6 x y+y^{2}-8 y$$

That's it, you are done for now. Give yourself a pat on the back. You might want to treat yourself by taking the quiz. 🤯