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Expanding Brackets

Learn how to multiply out or expand brackets successfully in this lesson. Practice mental arithmetic and solve examples with positive and negative numbers. Gain confidence in your ability to expand brackets.

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Expanding Brackets

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  1. Expanding Brackets

  2. 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 outbrackets successfully. For example you should be able to multiply out the following: 4(x + 7) = 3(y – 5) = 6a(a + 2) = 2b(3 – 2b) =

  3. Mental Arithmetic 35 x 7 = ?

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

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

  6. Mental Arithmetic 5 x 99 = ?

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

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

  9. Can you find the area of this rectangle (in your head)? 27cm 8cm 160cm2 56cm2 20cm 7cm Answer: 216 cm2

  10. What is the area of this rectangle? x cm 7 cm Answer: 7x cm2

  11. What is the area of this rectangle? Can you write your answer in two different ways? a + 5 cm 20 4 cm 4a a 5 Answer: 4(a + 5) cm2 or 4a + 20 cm2 So 4(a + 5) = 4a + 20

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

  13. 3(a + 4) = 7(b + 2) = 6(x + 5) = 8(y + 3) = 4(x + 10) = 2(x + 2) = 5(8 + d) = (x + 3) = 3a + 12 7b + 14 6x + 30 8y + 24 4x + 40 2x + 4 40 + 5d x + 3 ExamplesTry these on your whiteboard

  14. 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 x2 – 5x 6a2 – 8ab Expanding BracketsExamples With Negative Numbers

  15. 3(a – 4) = 2(b – 7) = 7(s – 5) = 8(m – 3) = -6(x + 5) = -5(w + 2) = -8(y – 3) = -(x + 3) = x(x + 1) = x(x – 4) = 2x(x - 2) = 5d(8 + d) = 3x(2x + 3) = 4a(3 – 4a) = k(k - l) = 2b(3a – 5b) = ExamplesTry these on your whiteboard

  16. 3a – 12 2b – 14 7s – 35 8m – 24 -6x – 30 -5w – 10 -8y + 24 -x – 3 x2 + x x2 – 4x 2x2 – 4x 40d + 5d2 6x2 + 9x 12a – 16a2 k2 – lk 6ab – 10b2 Answers

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

  18. 4(x + 7) = 3(y – 5) = 6a(a + 2) = 2b(3 – 2b) = 4x + 28 3y – 15 6a2 + 12a 6b – 4b2 Check Your Understanding

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