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2. Forming (Examples 1) Expressions and Terms Forming Expressions An algebraic expression can be formed from a given word problem as in the example questions below. (a) x + 6(b) x + 12(c) 2 x 1. Charlotte is x years old. How old will she be in: (a) 6 years time. (b) 12 years time. (c) When she is twice as old. 2. Simon is y years old. (i) How old was he: (a) 3 years ago. (b) 7 years ago. (ii) How old will he be when he is 3 times as old as he is now? (a) y - 3 (b) y - 7 (d) 3y Example Questions

3. Questions 1 Expressions and Terms Questions 1. The three strips of wood have lengths as shown. Write expressions for the following situations: (a) The length of the new strip if the first two strips were joined together. (b) The length of the new strip that is 3 times as long as the first. (c) The length of the new strip when the last strip is sawn off the first. (d) The length of the new strip when 5 of the first and 4 of the last are joined. l cm 3 cm 2 cm (a) l + 3 cm (b) 3l cm (c) l - 2 cm 24 Books 2. (a) How many books are there in n boxes? (b) How many books are there in n boxes and half a box? (a) 24 n (b) 24 n + 12 (d) 5 l + 8 cm

4. Defining An Algebraic expression, like the first two shown below, are made up of terms. Expressions are not equations because they do not contain an equals sign. (a) 3x + 5 (b) 5x - 4y - 6 (c) 4x - 1 = 7 2 term expression3 term expressionEquation term in x constant term term in y In (a) the co-efficient of x = 3 In (b) the co-efficient of x = 5 In (b) the co-efficient of y = - 4 Within an expression, each term takes the value of the operation immediately in front of it. So in the example below, which has four terms, the values are: 7x + 5 - 3x - 8 + 7x + 5 - 3x - 8 Like terms can be collected together to simplify an expression. = 4x - 3 + 4x + 4x - 3 Expressions and Terms

5. Examples 2 6p + 8 - 3x - 4 + 3p Example Question 1 In each of the examples below we will simplify the given expression by collecting like terms. = 9p - 3x + 4 7 - 5y - 4y - 2x + 5x Example Question 2 = 3x - 9y + 7 -3 +a + 7a - 2b + 5a + 3b + 1 Example Question 3 = 13a + b - 2 3x 2 - x - x 2 +4x Example Question 4 = 2x 2 + 3x 2ab - 1 + 3ab + 2 + ab Example Question 5 = 6ab + 1 Expressions and Terms

6. Questions 2 Simplify the following expressions: = 5x + 11 = 6x - 2 = 5p + q + 3 = 6y 2 + 5x - 3 = 8ab + 8 = 4x 2 + 2x - 7 = - 12p - 6 (a) 2x + 5 + 3x + 6 (b) 5x - 8 + x + 6 (c) 7p - 3 + p + 6 - 3p + q (d) y 2 - 4 + 5y 2 + 7x + 1 - 2x (e) ab + 3 - 4 + 7ab + 9 (f) -2x +3x 2 - 7 + 5x + x 2 - x (g) 1 - 2p - 5 - 3p - 8 - 7p + 6 (h) 4m + 8 + 3n 2 - 5m - n 2 - 1 = 2n 2 - m + 7 Expressions and Terms

7. Examples 3 In each of the examples below we will find the perimeter of the shape and simplify. Example Question 6 5 x x 5 = x + 5 + x + 5 = 2x + 10 x 3 x + 2 Example Question 7 = x + x + 2 + 3 = 2x + 5 Expressions and Terms

8. Questions 3 Find the perimeter of the shape and simplify. Question 1 = 7x + 6 x Question 2 2x2x 2x + 3 x x - 2 5 7 = 2x + 10 Expressions and Terms

9. Multiplying Terms (a) 6 x 3x Terms can be multiplied together as in the following examples: Note that we write a x b x c as abc Multiplying Terms = 18x (b) 5y x 4 = 20y (e) 2a x 3b = 6ab (c) 3x x 2x = 6x 2 (d) x x x 2 = x 3 (f) xy x 3y = 3y 2 x (g) 3a x 3a 2 = 9a 3 (h) 5p x 2p x p = 10p 3 (k) -5a x 3a = -15a 2 (i) 4y 2 x 3y = 12y 3 (j) -2 x 3x 2 = -6x 2 (l) -4x 2 y x xy 2 = - 4x 3 y 3 Expressions and Terms

10. Questions 4 Expressions and Terms Write the following in a more simplified form. Multiplying Terms = 48p = 15m = 12pq = 14x 2 = 2x 3 (a) 6 x 8p (b) 5m x 3 (e) 4p x 3q (c) 2x x 7x (d) x 2 x 2x (f) 3xy x 2x = 6x 2 y = 3m 3 = 6ab 2 c = -9a 3 = 7y 3 = -12x 2 (g) m x 3m 2 (h) 3a x 2b 2 x c (k) -3a 2 x 3a (i) y 2 x 7y (j) 4 x - 3x 2 (l) -2p 2 x pq 2 = - 2p 3 q 2

11. Worksheet 1 Expressions and Terms Questions 1. The three strips of wood have lengths as shown. Write expressions for the following situations: (a) The length of the new strip if the first two strips were joined together. (b) The length of the new strip that is 3 times as long as the first. (c) The length of the new strip when the last strip is sawn off the first. (d) The length of the new strip when 5 of the first and 4 of the last are joined. l cm 3 cm 2 cm 24 Books 2. (a) How many books are there in n boxes? (b) How many books are there in n boxes and half a box? Worksheet

12. Worksheet 2 (a) 2x + 5 + 3x + 6 (b) 5x - 8 + x + 6 (c) 7p - 3 + p + 6 - 3p + q (d) y 2 - 4 + 5y 2 + 7x + 1 - 2x (e) ab + 3 - 4 + 7ab + 9 (f) -2x +3x 2 - 7 + 5x + x 2 - x (g) 1 - 2p - 5 - 3p - 8 - 7p + 6 (h) 4m + 8 + 3n 2 - 5m - n 2 - 1 Questions 1 2x2x 2x + 3 x x - 2 5 7 x Questions 2 1 2 Worksheet

13. Worksheet 3 (a) 6 x 8p (b) 5m x 3 (e) 4p x 3q (c) 2x x 7x (d) x 2 x 2x (f) 3xy x 2x (g) m x 3m 2 (h) 3a x 2b 2 x c (k) -3a 2 x 3a (i) y 2 x 7y (j) 4 x - 3x 2 (l) -2p 2 x pq 2 Questions 3 Worksheet