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Expanding Brackets

Expanding Brackets. Objectives. By the end of the lesson you must understand what it is to multiply out (or 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 own

  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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