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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