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Expressions
and Formulae
- Simplifying expressions
- Simplifying expressions with one variable: Xa +
Ya + Za = (X + Y + Z)a e.g. 15a – (5a + 6a) = 15a –
11a = 4a
- Simplifying expressions with multiple variables:
Wb + Xa + Ya + Zb = (X + Y)a + (W + Z)b e.g. 15a +
6b – (5b + 6a) = (15a – 6a) + (6b - 5b) = 9a + b
- Simplifying expressions with one variable: Xa +
Ya + Za = (X + Y + Z)a e.g. 15a – (5a + 6a) = 15a –
11a = 4a
- Expanding brackets
- x(a + b) = xa + xb .
2x(4 + 2) = 2x(6) = 12x .
- x(a + b) = xa + xb .
2x(4 + 2) = 2x(6) = 12x .
- Factorising brackets
- Use highest common factors of all the numbers in an expression / a formula to
see what you should factorise with. For example if it is 6x + 4xy you can factorise
to make it 2x(3 + 2y) because 2x is the HCF. 16x_ + 4x = 4x(4x + 1)
- Difference of two squares: If a formula is Ax_ - y_ then you can
factorise as (x+y)(Ax - y) or ( Ax +y)( Ax - y)
- Use highest common factors of all the numbers in an expression / a formula to
see what you should factorise with. For example if it is 6x + 4xy you can factorise
to make it 2x(3 + 2y) because 2x is the HCF. 16x_ + 4x = 4x(4x + 1)
- Quadratic equations
- 2x_ + 8x +8 = (2x + 4)(x+2) because 4*2=8 and 4 + (2*2) = 8
- 2x_ + 8x +8 = (2x + 4)(x+2) because 4*2=8 and 4 + (2*2) = 8
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