Introducing Algebra
- 1. Introducing algebraBTEOTSSSBAT simplify equations and use substitution
- 2. In algebra:x + 2 means two more than xx – 3 means three less than xx + y means add together x and y3x 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 4x² means x multiplied by itself: x x
- 3. Write down the algebraic expression that means:3 more than y5 less than sx divided by yw multiplied by 4f multiplied by 3 and divided by t4 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 subtractedFor example2a + 4a = 6abut 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. BracketsSometimes 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 4This can be simplified to 3x + 12.
- 7. ExampleExpand 3(2x + 5)Here the 3 multiplies the 2x as well as the 5This 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. SubstitutionSubstituting in a formula means replacing the letters by numbersFor example, in the formula A = lwIf 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 ofa)a + b + y b) ax c) by 3a – 4 e) bx + 2 f) 3xy3x + y h) 2b – x i) 2ax + 3yj) ab – x k) ay + bxl) 2axy