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 × 12It 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. 🤯

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