2.1, 2.2 Algebra and Manipulation

Front

Combining algebraic terms:

Multiplying (or dividing) will change the POWER

Adding (or subtracting) will change the NUMBER IN FRONT

Back

e.g.

a + a + a = 3a

a x a x a = a³

Front

Adding and subtracting algebra:

The sign in front of the term goes with it

e.g. Simplify 4a + 2b - 7a

Back

a terms are +4a and -7a = -3a

b terms are just 2b

Simplifies to -3a + 2b

Front

Algebraic shorthand

What does 3ab mean?

Back

3 x a x b

Front

Multiplying algebraic terms with more than one element

e.g. 2a x 3ab

Back

Multiply each part together individually then combine them together.

e.g. numbers 2 x 3 = 6

a terms a x a = a²

b terms just b

Combine to 6a²b

Front

PROCESS:

Expanding brackets

e.g. 2y (3 - 4y)

Back

The thing outside the bracket multiplies each thing inside including the sign.

e.g. 2y (3 - 4y)

= 2y x 3 - 2y x 4y

= 6y - 8y²

Front

PROCESS:

Factorise

e.g. Factorise 8ab - 12b²

Back

Factorise is the opposite of expand - going from no brackets to having brackets

Find the biggest thing that goes into each term. You need to look at the numbers and the letters. Write that and open a bracket. Then ask 'what do I have to multiply that by to get what is in the question?'

e.g. Factorise 8ab - 12b²

Biggest number in both is 4

Biggest a in both is none

Biggest b in both is b

So 4b goes outside the bracket

=4b(.....

What do I multiply 4b by to get 8ab? 2a.

=4b(2a.....

What do I multiply 4b by to get 12 b²? 3b.

=4b(2a - 3b)

Front

Back

First x First

First x Second

Second x First

Second x Second

The signs go with the thing that follows that sign, and joins each component together.

Then combine the two middle terms.

e.g. x² - 3x + 2x -6

= x² - x - 6

Front

PROCESS:

Factorise a quadratic expression

e.g. x² + 6x + 8

Back

You are looking for two FACTORS OF THE LAST NUMBER that add up to the middle number.

List your factors, pick the pair that works and put into brackets.

e.g. 8 = 1x8 or 2x4

2+4 = 6 so we use those.

e.g. (x + 2)(x + 4)