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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