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**Lesson 8 Expand and Simplify. Mathswatch 103**

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**Write 14 as a percentage of 20 What is 3y x 5y ? Convert 2500g to kg**

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

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**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)

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**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) x - 9 3 3x -27 Final Ans: 3x -27

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**Lesson 8 Expand and Simplify. Mathswatch 103**

+ 7 Expand the following expression x(x +7) x² +7x Final Ans: x² + 7x

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**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

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**Answer: We do two separate 2 x 1 grids then collect up like things.**

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. x - 4 5 x - 3 3 + 5x - 20 3x - 9 + 5x - 20 3x - 9 Watch out for negatives. Final Ans: 8x - 29

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**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) (5x - 3) - 7(2x + 4) + 5x (a) 7x + 26 (b) 5x - 1 (c) 17x - 8 (d) x (e) 10x + 19 (f) x - 25

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**Lesson 8 Expand and Simplify. Mathswatch 103**

What’s the difference? a) 4(x + 6) + 2(x – 7) b) (4x+6)(2x-7) So how do we expand when we have two brackets right next to each other then?...... Questions 1 Answer: Just the same but a 2 x 2 grid.

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**Final Ans: - x x²- x - 30 x² +5x - 6x -30**

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

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**Lesson 8 Expand and Simplify. Mathswatch 103**

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

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**Lesson 8 Expand and Simplify. Mathswatch 103**

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

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**Lesson 8 Expand and Simplify. Mathswatch 103**

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**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)

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Expanding Brackets Multiply the contents of the bracket by what is immediately outside it E.g. 3(a+4) 3a3a + 12 3 x a + 3 x 4.

Expanding Brackets Multiply the contents of the bracket by what is immediately outside it E.g. 3(a+4) 3a3a + 12 3 x a + 3 x 4.

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