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Lesson 8 Expand and Simplify. Mathswatch 103 GCSE Maths Starter 8 1) Describe the correlation. 2. Write 14 as a percentage of 20 3. What is 3y x 5y ? 4. Convert 2500g to kg 5) Solve the equations below: Lesson 8 Expand and Simplify. Mathswatch 103 • To simplify expressions by collecting like terms. • To expand individual single brackets. • To expand and simplify more than one single bracket. EXTN: To expand and simplify double brackets. (Grade C) Lesson 8 Expand and Simplify. Mathswatch 103 By expanding brackets we mean multiply each term in the bracket by the term outside. Because it is multiplying, we use the grid method for this. Expand the following expression 3(x - 9) 3 Final Ans: x -9 3x -27 3x -27 Lesson 8 Expand and Simplify. Mathswatch 103 x Expand the following expression x x² x(x +7) Final Ans: x² + 7x +7 +7x Lesson 8 Expand and Simplify. Mathswatch 103 Now you try these…… (You have 5 mins max and must show your working) Expand each of the following: (a) 3(x + 8) (b) 7(x + 2) (c) 2(5x - 2) (d) 8(2x - 3) (e) 7(y + 1) (f) 9(3k - 8) (a) 3x + 24 (b) 7x + 14 (c) 10x - 4 (d) 16x - 24 (e) 7y + 7 (f) 27k - 72 Questions 1 Lesson 8 Expand and Simplify. Mathswatch 103 What happens when we have two individual brackets with a plus or minus between them like below: 5(x - 4) + 3(x- 3) Answer: We do two separate 2 x 1 grids then collect up like things. 5 5x -4 - 20 + + x 3 x -3 3x -9 5x - 20 3x - 9 Final Ans: 8x - 29 Watch out for negatives. Lesson 8 Expand and Simplify. Mathswatch 103 Now some for you to try: How many can you do in 5 minutes? (with workings!) Expand and simplify each of the following: (a) 4(x + 5) + 3(x + 2) (b) 2(3x + 1) - (x + 3) (c) 3(5x - 2) + 2(x - 1) (d) -7(x - 2) - 2(x - 1) (e) 5(3x - 1) - 4(2x - 3) + 3(x + 4) (f) 9 + 2(5x - 3) - 7(2x + 4) + 5x (a) 7x + 26 (b) 5x - 1 (c) 17x - 8 (d) 16 - 9x (e) 10x + 19 (f) x - 25 Lesson 8 Expand and Simplify. Mathswatch 103 What’s the difference? a) b) 4(x + 6) + 2(x – 7) (4x+6)(2x-7) So how do we expand when we have two brackets right next to each other then?...... Answer: Just the same but a 2 x 2 grid. Questions 1 Lesson 8 Expand and Simplify. Mathswatch 103 Expand and simplify the following expression (x + 5)(x - 6) x x -6 x² - 6x Final Ans: x²-- x - 30 +5 +5x -30 Watch out for negatives. Lesson 8 Expand and Simplify. Mathswatch 103 Expand and simplify the following expression (2a + 3)(4a + 2) 2a +3 4a 8a² +12a +2 +4a +6 Final Ans: 8a²+ 16a +6 Lesson 8 Expand and Simplify. Mathswatch 103 Now some for you to try: How many can you do in 5 minutes? (with workings!) Expand and simplify each of the following: Watch out for negatives. (a) (x + 5)(x + 2) (a) x² + 5x + 2x + 10 (a) x² + 7x +10 (b) (x - 1)(x + 3) (b) x² -1x +3x -3 (b) x² +2x-3 (c) (x - 6)(x + 1) (c) x² - 6x +1x -6 (c) x² - 5x -6 (d) (x - 2)(x - 3) (d) x² - 2x – 3x +6 (d) x² -5x +6 (e) (3x + 1)(2x + 3) (e) 3x²+2x +9x+3 (e) 3x²+11x+3 (f) (5x - 3)(2x + 4) (f) 10x²-6x+20x-12 (f) 10x²+14x-12 Lesson 8 Expand and Simplify. Mathswatch 103 Lesson 8 Expand and Simplify. Mathswatch 103 • To simplify expressions by collecting like terms. • To expand individual single brackets. • To expand and simplify more than one single bracket. EXTN: To expand and simplify double brackets. (Grade C)