SQA National 5 (NAT5) Maths - Simplifying Expressions
Channel: Eng Maths
Date: 2021-04-08

In this video, we’re going to look at how to simplify algebraic expressions. Before we get started on simplifying, a few things to remember: 

(1) we always use a curly x for the letter x in algebra. 

(2) We don’t really use the multiplication sign. 3a is how we write 3 X a. 

(3) Instead of using the division sign, we use fractions.

3 divided by 2 is written as 3/2. In algebra, we are often asked to simplify something or to put it in its simplest form. Generally speaking, the simpler it is, the easier it is to use. We just need to combine like terms. Simplify fully 5a - 2b + 3a + 2 + 4b - 7. We combine the a’s to get 8a, and we combine the b’s (including the sign in front of each term) to get 2b. And finally, we combine the numbers to get -5. Answer: 8a + 2b - 5. We cannot combine different letters so that is the simplest form. This expression may represent 8 apples and 2 bananas, which are different things so cannot be added together. For division, you can cancel numbers exactly as you would with fractions. And also you can also cancel down letters. 

So if you have a to the power of 5 in the numerator and a to the power of 3 in the denominator, we can cancel these down to end up with a to the power of 2 in the numerator and no a's left in the denominator. We can also simplify by factoring into brackets or by expanding brackets - which are skills we will look at in other videos.

When I was studying I found these books really helpful:
Engineering Mathematics https://amzn.to/3wOd4gG​
National 5 Maths: SQA Revision Guide https://amzn.to/39QRpKY