Simplifying Expressions

Collecting like terms

When simplifying algebraic expressions, you can only add terms that a like (the same)

Examples:

b + b + b = 3b

a + b + a + b = 2a + 2b

5w + 3w = 8w

y + y² + 2y² = y + 3y²

Equations and Formulae

Difference between equations and formulae

An equation contains unknown quantities; for example,

3x + 2 = 11.

This equation can be solved to determine x.

A formula links one quantity to one or more other quantities; for example,

C = 2πr

The formula can be used to determine C for any given value or r

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Factorising

Factorising

Factorising (put in brackets) can be said to be the 'opposite of expanding brackets'.

To factorise an expression live 3w+12 you find out the highest factor the terms have in common.
In this case it is 3. That means 3 needs to be outside the bracket.
Then you find out what you multiply by 3 to get 3w and what you multiply by 3 to get 12.

3 x w = 3w and 3 x 4 = 13 since 3 is the highest factor both terms have in common.

so factorising 3x+12 gives 3(w+4).

Examples:

Factorise the following expressions

1) 4y + 12
The highest common factor is 4, so 4 has to be outside the bracket.
4 x y = 4y and 4 x 3 = 12

so 4y + 12 = 4(y + 3)

2) 30b + 42
The highest common factor is 6, so 6 has to be outside the bracket.
6 x 5b = 30b and 6 x 7 = 42

so 30b + 42 = 6(5b + 7)

3) 6v + 15w
The highest common factor is 3, so 3 has to be outside the bracket.
3 x 2v = 6v and 3 x 5w = 15w

s0 6v + 15w = 3(2v + 3w)

Expanding Brackets

Expanding or multipying out brackets.

To expand a bracket such as 3(x +2) you multiply every term in the bracket by 3 making it 3x + 6.

Examples

Expand these brackets:

1) 4(y + 3) = 4y + 12
2) 6 (5b + 7) = 30b + 42
3) 3 (2v + 5w) = 6v + 15w

Spot the mistake

Spot the mistake:

3(x + 5) = 3x + 5

4(xy + y) = 4x + 4y

7(w - 4) = 7w + 28

6(a + 2) = 6a + 12

6a + 7a + 2b = 15ab

Solving Simple Linear Equations

A lot of students seem to find it difficult to solve equations. The act of solving equations is all about doing the same thing to both sides of the equation and making sure you end up with the letters on one side and the numbers on the other side of the equation.

For Example:

Find the value of y in these equations:

y + 3 = 10
Subtract 3 from both sides
y = 7

y – 3 = 10
Add 3 to both sides
y = 13

3) 4y + 5 = 21
Subtract 5 from both sides
4y = 16
Divide both sides by 4
y = 4

In the first equation we subtracted 3 because it was + 3. So the general rule is to use the inverse operation.