Chapter 11: Factorising and Formulae
Factorising
- Factorising is the opposite of expanding brackets
- You need to look for the largest factors you can take out of every term in the expression
Factorising x^2 + bx + c
- You need to write the expression with two brackets
- x^2 + 7x + 10
- You need to find two numbers which add up to 7 and multiply to make 10
- 5+2=7
- 5x2=10
- When factorising x^2 + bx + x use this table to help find the two numbers
| b | c | Factors |
|---|
| Positive | Positive | Both numbers positive |
| Positive | Negative | Bigger number positive and smaller number negative |
| Negative | Negative | Bigger number negative and smaller number positive |
| Negative | Positive | Both numbers negative |
Factorising ax^2 + bx + x
- One of the brackets must contain a ax term
- Try pairs of numbers which have a product of c
- Check each pair by multiplying out the brackets
Difference of two squares
- You can factorise expression that are written as something^2 - something else^2
- A formulae is a mathematical rule
- You can write formulae using algebra
- This label shows a formula for working out the cooking time of a chicken
- You can write this formula using algebra using units
Working in out
- Substitute the values for u and t into the formula
- If you use brackets then you’re less likely to make a mistake
- This is really important when there are negative numbers involved
- Remember BIDMAS for the correct priority of operations
- You need to do:
- Indices
- Multiplication
- Subtraction
- Don’t try to do more than one operation on each line of working
Problem solved tips
- You are only given the dimensions of the rectangle
- You need to infer the height of the triangle
- The angle of the slope is x and the base of the triangle is 2x so the height of the triangle must be x. Write this dimension on your diagram
- Use these dimensions to write an expression for the area of the triangle