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Lesson 8 Expand and Simplify. Mathswatch 103

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GCSE Maths Starter 8 2.Write 14 as a percentage of 20 3.What is 3y x 5y ? 4.Convert 2500g to kg 1) Describe the correlation. 5) Solve the equations below:

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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

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x x -27 Expand the following expression 3(x - 9) Lesson 8 Expand and Simplify. Mathswatch 103 3x -27 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. Final Ans:

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x+ 7 x x² + 7x Expand the following expression x(x +7) Lesson 8 Expand and Simplify. Mathswatch 103 x²+7x Final Ans:

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Questions 1 Now you try these…… (You have 5 mins max and must show your working) Expand each of the following: (a) 3x + 24 (b) 7x + 14 (c) 10x - 4 (d) 16x - 24 (e) 7y + 7 (f) 27k - 72 (a) 3(x + 8) (b) 7(x + 2) (c) 2(5x - 2) (d) 8(2x - 3) (e) 7(y + 1) (f) 9(3k - 8) Lesson 8 Expand and Simplify. Mathswatch 103

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x x - 9 What happens when we have two individual brackets with a plus or minus between them like below: 5(x - 4) + 3(x- 3) Lesson 8 Expand and Simplify. Mathswatch 103 5x - 20 Final Ans: Answer: We do two separate 2 x 1 grids then collect up like things. x x x x - 29 Watch out for negatives.

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Now some for you to try: How many can you do in 5 minutes? (with workings!) Expand and simplify each of the following: (a) 7x + 26 (b) 5x - 1 (c) 17x - 8 (d) x (e) 10x + 19 (f) x - 25 (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 Lesson 8 Expand and Simplify. Mathswatch 103

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Questions 1 What’s the difference? a) 4(x + 6) + 2(x – 7) a) 4(x + 6) + 2(x – 7) Lesson 8 Expand and Simplify. Mathswatch 103 b) (4x+6)(2x-7) b) (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.

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x+5 x x Expand and simplify the following expression (x + 5)(x - 6) Lesson 8 Expand and Simplify. Mathswatch 103 x²+5x - - 6x-30 x²- x - 30 Final Ans: Watch out for negatives.

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2a+3 4a +2 16a Expand and simplify the following expression (2a + 3)(4a + 2) Lesson 8 Expand and Simplify. Mathswatch 103 8a²+12a +4a+6 8a²+ 16a +6Final Ans:

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Now some for you to try: How many can you do in 5 minutes? (with workings!) Expand and simplify each of the following: (a) x² + 7x +10 (b) x² +2x-3 (c) x² - 5x -6 (d) x² -5x +6 (e) 3x²+11x+3 (f) 10x²+14x-12 (a) (x + 5)(x + 2) (b) (x - 1)(x + 3) (c) (x - 6)(x + 1) (d) (x - 2)(x - 3) (e) (3x + 1)(2x + 3) (f) (5x - 3)(2x + 4) Lesson 8 Expand and Simplify. Mathswatch 103 (a) x² + 5x + 2x + 10 (b) x² -1x +3x -3 (c) x² - 6x +1x -6 (d) x² - 2x – 3x +6 (e) 3x²+2x +9x+3 (f) 10x²-6x+20x-12 Watch out for negatives.

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Lesson 8 Expand and Simplify. Mathswatch 103

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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

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