# Year 10 Maths Higher Tier Revision

- Created by: xoxbeckywxox
- Created on: 28-04-15 20:12

**Simplifying expressions**

**Gather all similar expressions together: Group all letters**

4a+a-7d+6d= 5a-d

4a+a2-a=3a+a2 You can't add 4a and a2, so they are separate, just as you can't add a2 and a3.

**Indices**

a2 x a3=a5 a4 / a2=a2 (a2)3=a6

a-2 x a3=a a-4 / a2=a-6 (a-2)3=a-6

a2 x a-3=a-1 a4 / a-2=a6 (a2)-3=a-6

a-2 x a-3=a-5 a-4 / a-2=-2 (a-2)-3=a6

3 to the power of -3= 1/27 (3x3x3=27 reciprocal)

25 to the power of 1/2=5 (square root of 25)

27 to the power of 2/3= 9 (cube root of 27=3 square it)

**Expanding brackets**

**single brackets**- times the term on the outside of the bracket by the terms on the inside of the bracket. eg 3(a+2)=3a+6

**Double brackets- FOIL**

**F** irst: Multiply the first term in each bracket

**O** utside: Multiply the terms on the outside of the expression

**I **nside: Multiply the terms on the inside of the expression

**L** ast: Multiply the last term in each bracket

THEN SIMPLIFY EG: (3a+2)(2a+6)

F O I L

6a2 18a 4a 12

6a2+18a+4a+12= 6a2+22a+12

**Factorising Brackets**

**Single Brackets- **Look for a common factor and put it outside the brackets. Put the unique terms inside the brackets eg: 18a+12=6(3a+2)

**Double Brackets- ax2+bx+c**

**If a=1,** you can factorise using a sum and product approach.

Eg: x2+12x+35, you need…

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