1. Saturday, 16 September 2006 ©RSH Algebra

2. Saturday, 16 September 2006 ©RSH Expressions and Equations An equation has an equal sign. An expression doesn’t. Expressions and Equations An equation has an equal sign. An expression doesn’t. Notes Which are expressions and which are equations ? 2x + 1 = 8 3x – 8 4 – x 7x – 6 = 7 Which are expressions and which are equations ? 2x + 1 = 8 3x – 8 4 – x 7x – 6 = 7 Equation Expression

3. Saturday, 16 September 2006 ©RSH Using Letters for numbers Write an expression for this statement: I start with x, double it and then add 8 Using Letters for numbers Write an expression for this statement: I start with x, double it and then add 8 Notes doubleadd 8 x 2x 2x + 8 The expression is: 2x + 8

4. Saturday, 16 September 2006 ©RSH Exercise 1.Write expressions for the following: a)2x – 7 b)2(x + 5) c)7x – 5 d)2(x + y) e)(x + 6) 2 a)Start with x, double it and then subtract 7 b)Start with x, add 5 then double the result c)Start with x, multiply by 7 then take away 5 d)Start with x, add y then double the result e)Start with x, add 6 then square the result

5. Saturday, 16 September 2006 ©RSH Collecting like terms In the expression 2x + 1, both 2x and 1 are called terms. Terms can be collected if they are the same type. Collecting like terms In the expression 2x + 1, both 2x and 1 are called terms. Terms can be collected if they are the same type. Notes Examples 1.2x + 3x + 1 = 5x + 1 2.4x + 3 + 2x –1 = 6x + 2 3.6x + 7y – 2x – 4y = 4x + 3y x and y are unlike terms 4.x² + 3x² + x + 4x = 4x² + 5x x² and y² are unlike terms Examples 1.2x + 3x + 1 = 5x + 1 2.4x + 3 + 2x –1 = 6x + 2 3.6x + 7y – 2x – 4y = 4x + 3y x and y are unlike terms 4.x² + 3x² + x + 4x = 4x² + 5x x² and y² are unlike terms

6. Saturday, 16 September 2006 ©RSH Exercise 1.Collect like terms a)5x + 8 b)9x + 5 c)5x – 12 d)7a + 11b e)4x² + 2x + 11 a)2x + 3 + 3x + 5 b)5x – 3 + 4x + 8 c)9x – 9 + 2x – 3 – 6x d)12a + 4b + 7b – 5a e)x² + 5x + 4 – 3x + 7 + 3x²

7. Saturday, 16 September 2006 ©RSH Expanding Brackets (Multiplying out brackets) Here are some examples of expanding brackets. Everything inside the bracket is multiplied by the term outside. Expanding Brackets (Multiplying out brackets) Here are some examples of expanding brackets. Everything inside the bracket is multiplied by the term outside. Notes Examples 1.2(x + 1) = 2x + 1 2.3(2x – 3) = 6x – 9 3.-4(x + 4) = -4x –16 4.-2(2x – 3) = -4x + 6 5.x(x + 2) = x² + 2x Examples 1.2(x + 1) = 2x + 1 2.3(2x – 3) = 6x – 9 3.-4(x + 4) = -4x –16 4.-2(2x – 3) = -4x + 6 5.x(x + 2) = x² + 2x Careful with signs

8. Saturday, 16 September 2006 ©RSH Exercise 1.Expand these brackets a)2x + 20 b)6x – 27 c)8x – 12 d)15 + 15x e)-20x – 30 f)-15 + 6x g)x² + 9x h)2x² - 6x i)12x² + 6x j)2x 3 – 2x² a)2(x + 10) b)3(2x – 9) c)4(2x – 3) d)5(3 + 3x) e)-10(2x + 3) f)-3(5 – 2x) g)x(x + 9) h)2x(x – 3) i)3x(4x + 2) j)2x²(x – 1)

9. Saturday, 16 September 2006 ©RSH Expanding Brackets and simplifying Easy – expand the brackets first and then collect like terms Expanding Brackets and simplifying Easy – expand the brackets first and then collect like terms Notes Examples 1.2(x + 1) + 3(x + 2) = 2x + 2 + 3x + 6 = 5x + 8 2.3(x – 2) – 2(x + 1)= 3x – 6 –2x –2 = x - 8 Examples 1.2(x + 1) + 3(x + 2) = 2x + 2 + 3x + 6 = 5x + 8 2.3(x – 2) – 2(x + 1)= 3x – 6 –2x –2 = x - 8 Careful with signs

10. Saturday, 16 September 2006 ©RSH Exercise 1.Expand and simplify a)2x + 4 + 4x + 4 = 6x + 8 b)2x – 6 + 3x + 9 = 5x + 3 c)7x – 14 + x + 4 = 8x – 10 d)6x – 12 – 2x – 18 = 4x – 30 e)4 + 2x + 3x – 3 = 5x + 1 a)2(x + 2) + 4(x + 1) b)2(x – 3) + 3(x + 3) c)7(x – 2) + (x + 4) d)6(x – 2) – (2x + 9) e)2(2 + x) + 3(x – 1)