1. Difference between Expression and Equation?
An Expression is made up of letters, numbers and operators but has NO EQUALS sign – expressions represent a number
𝐸𝑥𝑎𝑚𝑝𝑙𝑒𝑠 𝑜𝑓 𝐸𝑥𝑝𝑟𝑒𝑠𝑠𝑖𝑜𝑛𝑠: 2𝑥+3, 𝑎+2𝑏+3𝑐, 𝑥 2 +3𝑥−4
An Equation has an equals sign – it says that two things are equal
𝐸𝑥𝑎𝑚𝑝𝑙𝑒𝑠 𝑜𝑓 𝐸𝑞𝑢𝑎𝑡𝑖𝑜𝑛𝑠: 𝑥+3= 𝑥 2 +3𝑥−4=0
An Expression can only be SIMPLIFIED
An Equation can be SOLVED (𝑥 = something)

2. L.O. To be able to solve Quadratic Equations
We already know how to factorise quadratic expressions!
There are several ways to solve a quadratic equation
Factorising
Graphically
Completing the square
The quadratic formula

3. Starter (𝒙−𝟔)(𝒙−𝟒) (𝒙+𝟓)(𝒙−𝟏𝟐) (𝒙+𝟖)(𝒙−𝟖)
Factorise the following quadratics:
𝑥 2 −10𝑥+24
𝑥 2 −7𝑥−60
𝑥 2 −64
(𝒙−𝟔)(𝒙−𝟒)
(𝒙+𝟓)(𝒙−𝟏𝟐)
(𝒙+𝟖)(𝒙−𝟖)

4. Factorising Method
When using the factorising method to solve a quadratic equation, the equation must always equal zero
If it doesn’t, re-arrange the equation to make it equal to zero!

5. Quadratics
When solving a quadratic, you can have two, one or no values for 𝑥. This is because the curve of a quadratic equation can cross the x-axis (where 𝑦 = 0) at two, one or no places. 𝑦
This quadratic equation would have no possible solutions
This quadratic equation would have one possible solution
This quadratic equation would have two possible solutions 𝑥

6. Factorising Method Solve the equation: 𝑥 2 −10𝑥+24=0 𝑥−6 𝑥−4 =0
𝑥−6 𝑥−4 =0
𝑥−6=0 or 𝑥−4=0
𝑥=6 or 𝑥=4
1. Factorise
Since the two brackets multiplied together equals zero, at least one bracket must equal zero, so…
2. Solve the equations

7. Factorising Method Solve the equation: 𝑥 2 −10𝑥+25=0 𝑥−5 𝑥−5 =0
𝑥−5 𝑥−5 =0
𝑥−5=0 or 𝑥−5=0
𝑥=5

8. Factorising Method 𝑥 2 + 12𝑥 + 32 = 0 𝑥 2 - 49 = 0 𝑥 2 + 6𝑥 + 9 = 0
On your whiteboards, solve the following quadratic equations:
𝑥 𝑥 + 32 = 0
𝑥 = 0
𝑥 𝑥 + 9 = 0
𝑥 𝑥 + 36 = 0
𝑥 𝑥 – 44 = 0
𝑥 𝑥 – 30 = 0
𝑥 𝑥 – 27 = 0

9. Graded Worksheet