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Expanding Brackets

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Objectives By the end of the lesson you must understand what it is to multiply out (or expand) brackets. By the end of the lesson you should feel confident about your ability to multiply out brackets successfully. For example you should be able to multiply out the following: 4(x + 7) =3(y – 5) = 6a(a + 2) =2b(3 – 2b) =

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Mental Arithmetic 35 x 7 = ?

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Mental Arithmetic 35 x 7 = 245 How did you work it out?

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Mental Arithmetic 35 x 7 = (30 + 5) x 7 = 30x7 + 5x7 = 210 + 35 = 245

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Mental Arithmetic 5 x 99 = ?

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Mental Arithmetic 5 x 99 = 495 How did you work it out?

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Mental Arithmetic 5 x 99 = 5 x (100 – 1) = 5x100 – 5x1= 500 – 5 = 495

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27cm 8cm Can you find the area of this rectangle (in your head)? Answer: 216 cm 2 7cm20cm 56cm 2 160cm 2

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x cm 7 cm What is the area of this rectangle? Answer: 7x cm 2

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a + 5 cm 4 cm What is the area of this rectangle? Can you write your answer in two different ways? Answer: 4(a + 5) cm 2 or 4a + 20 cm 2 So 4(a + 5) = 4a + 20 a5 4a 20

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Expanding Brackets 4(a + 5) = 4a + 20 4(a + 5) = 4xa + 4x5 = 4a + 20

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Examples Try these on your whiteboard 1.3(a + 4) = 2.7(b + 2) = 3.6(x + 5) = 4.8(y + 3) = 5.4(x + 10) = 6.2(x + 2) = 7.5(8 + d) = 8.(x + 3) = 3a + 12 7b + 14 6x + 30 8y + 24 4x + 40 2x + 4 40 + 5d x + 3

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Expanding Brackets Examples With Negative Numbers 7(x – 3) = 5(2x – 4) = -3(3x + 5) = -2(4x – 3) = -(x – 7) = x(x – 5) = 2a(3a – 4b) = 7x – 21 10x – 20 -9x – 15 -8x + 6 -x + 7 x 2 – 5x 6a 2 – 8ab

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Examples Try these on your whiteboard 1.3(a – 4) = 2.2(b – 7) = 3.7(s – 5) = 4.8(m – 3) = 5.-6(x + 5) = 6.-5(w + 2) = 7.-8(y – 3) = 8. -(x + 3) = 9.x(x + 1) = 10. x(x – 4) = 11. 2x(x - 2) = 12. 5d(8 + d) = 13. 3x(2x + 3) = 14. 4a(3 – 4a) = 15. k(k - l) = 16. 2b(3a – 5b) =

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Answers 1.3a – 12 2.2b – 14 3.7s – 35 4.8m – 24 5.-6x – 30 6.-5w – 10 7.-8y + 24 8. -x – 3 9.x 2 + x 10. x 2 – 4x 11. 2x 2 – 4x 12.40d + 5d 2 13.6x 2 + 9x 14. 12a – 16a 2 15. k 2 – lk 16. 6ab – 10b 2

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Objectives By the end of the lesson you must understand what it is to multiply out brackets or expand brackets. By the end of the lesson you should feel confident about your ability to multiply out brackets or expand brackets succesfully.

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Check Your Understanding 4(x + 7) = 3(y – 5) = 6a(a + 2) = 2b(3 – 2b) = 4x + 28 3y – 15 6a 2 + 12a 6b – 4b 2

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AS Mathematics Algebra – Manipulation of brackets.

AS Mathematics Algebra – Manipulation of brackets.

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