This document introduces basic algebra concepts such as: - Expressions like x + 2 meaning two more than x - Simplifying expressions by collecting like terms - Using substitution to replace letters with numbers in expressions - Expanding expressions with brackets by multiplying numbers outside brackets by all terms inside

1. Introducing algebra BTEOTSSSBAT simplify equations and use substitution

2. In algebra: x + 2 means two more than x x – 3 means three less than x x + y means add together x and y 3x means three times x. We don’t usually use a multiplication sign! So 3x = 3 x means x divided by four. We can also write this as x 4 x² means x multiplied by itself: x x

3. Write down the algebraic expression that means: 3 more than y 5 less than s x divided by y w multiplied by 4 f multiplied by 3 and divided by t 4 less than x multiplied by 4

4. Simplifying (collecting like terms) To simplify an algebraic expression we have to collect like terms; only like terms can be added or subtracted For example 2a + 4a = 6a but 2a + 7b can’t be made any simpler.

5. Simplify these expressions (a) a + a + a (b) b + b + b – b (c) 3a + 2a (d) 3a + 2b – a

6. Brackets Sometimes brackets are used in expressions e.g. 3 (x + 4) A number next to a bracket multiplies everything inside the bracket. So, 3 (x + 4) is the same as 3  (x + 4) = 3 x + 3  4 This can be simplified to 3x + 12.

7. Example Expand 3(2x + 5) Here the 3 multiplies the 2x as well as the 5 This gives 3 × 2x + 3 × 5 = 6x + 15.

8. Multiply out the brackets and if necessary simplify the expression (a) 2 (x+3) (b) 4 (x + 4) (c) 5 (2x + 5)

9. Substitution Substituting in a formula means replacing the letters by numbers For example, in the formula A = lw If l = 3 and w = 4 Then lw = 3  4 = 12

10. Other examples: If a = 3 and b = 4, what is the value of a + b? Using substitution, a + b = 3 + 4 = 7 (ii) If a = 5, what is the value of 4a? Using substitution, 4a = 4  5 = 20 (iii) If x = 6 and y = 5, what is the value of 2xy? Using substitution, xy = x y = 6  5 = 30 and 2xy = 2 x y = 2  6  5 = 60

11. When a = 7, b = 4, x = 2 and y = 5, work out the values of a)a + b + y b) ax c) by 3a – 4 e) bx + 2 f) 3xy 3x + y h) 2b – x i) 2ax + 3y j) ab – x k) ay + bxl) 2axy