An expression is a collection of symbols such as X or Y and operations such as plus and minus they can also contain numbers. Expressions are important and can occur everywhere in mathematics they can be simplified to fewer parts as possible just to help them be more understandable.
Each part of an expression is called a term “a term” and this could be a number, a symbol, or a number with a symbol. Terms with the same symbols are “like terms” and it is possible for you to combine them.
2x + 2y – 7y + 6x
Here is an example expression the first step of calculating this is identifying the like terms. First, we highlight all of the numbers with the letter X and then we highlight all of the numbers containing the letter Y.
So here we would do 2X plus 6X giving us 8X. Then we have plus 2Y minus 4 Y. this would give us an answer of -2y.
Our new expression would not say 8x – 2y.
It doesn't matter how many numbers and letters are contained in the expression all you do is group them, so the same letters are in the same group and then you work out the equations accordingly. If we happen to end up with a #1 you don't need to include it it can often be referred to as just the letter alone.
4a – 6b + 2b - 3a + b
Step 1: 4a – 3a = 1a OR a …. -6b + 2b + b = -4b + b = -3b
Step 2: a – 3b
SIMPLIFYING EXPRESSIONS WITH MULTIPLCATION
When we are simplifying expressions, they include multiplication as an operation we first must separate all of the numbers from the letters.
6a x 2b (6a means 6 x a and 2b means 2 x b)
6 x a x 2 x b becomes 12 x ab which equals 12ab.
As you can see, we've separated the expression into the individual number and symbols involved then we can see that the product of multiplying six by two is 12, and multiplying a by b is ab. So, the simplified expression overall is 12ab.
SIMPLIFYING EXPRESSIONS WITH DIVISION
To simplify an expression involving division we must look for any possible cancellations this means looking to divide all the terms of the expression by the same number or letter.
4mp² ÷ 2p (the power of two symbol here is to remind you to multiply p by p)
The first step is to look for any chances to cancel the expression down and make it smaller this in turn will make easier to understand. Let's start by writing the division sum as a fraction.
MISSING IMAGE!!!
When we look at the expression written like this, we can see that we can divide the four and the two together we can also divide one of the p’s from the top and the bottom.
MISSING IMAGE!!!
When we divide 4 by 2 we're left with 2, when we divide the 2 by 2 we are left with 1 when we divide the P by P we're left with 1. Our new expression looks like this:
MISSING IMAGE!!!
SUBSTITUTION
Sometimes we can have algebraic expressions where the symbol values are provided, for example X can equal a particular number and Y could equal a different number. This is called “substituting” the values of the expression or evaluating the expression.
We most commonly use substituting expressions when calculating things like area or perimeter, we are given a formula to use to calculate from and we use the measurements provided to help work out the expression. For example: length x width and we would substitute those for 5cm x 10cm = 50cm².
This method could also be seen like this:
Substitute the values in this expression when x=2 and y=5.
2x – 2y + 4y + 3x
Step 1: group the like terms:
2x + 3x = 5x & -2y + 4y = 2y
Step 2: simplify.
5x + 2y
Step 3: substitute
5x = 5 x 2 = 10
2y = 2 x 5 = 10
Step 4: Calculate
10 + 10 = 20