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Expanding Brackets

Expanding Brackets. 3(a + 5) What does this mean? ‘add five to a then multiply the whole lot by three’ Or ‘three lots of a added to three lots of 5. Expanding Brackets. 3(a + 5). + 5. + 5. a. a. + 5. a. Expanding Brackets. 3(a + 5). + 5. + 5. a. a. + 5. a. 3(a + 5) =.

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Expanding Brackets

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  1. Expanding Brackets 3(a + 5) What does this mean? ‘add five to a then multiply the whole lot by three’ Or ‘three lots of a added to three lots of 5

  2. Expanding Brackets 3(a + 5) + 5 + 5 a a + 5 a

  3. Expanding Brackets 3(a + 5) + 5 + 5 a a + 5 a 3(a + 5) =

  4. Expanding Brackets 3(a + 5) + 5 + 5 a a + 5 a 3(a + 5) = (3 x a) +

  5. Expanding Brackets 3(a + 5) + 5 + 5 a a + 5 a 3(a + 5) = (3 x a) + (3 x 5) =

  6. Expanding Brackets 3(a + 5) + 5 + 5 a a + 5 a 3(a + 5) = (3 x a) + (3 x 5) = 3a + 15

  7. Expanding Brackets 6(2a + 4) + 4 + 4 + 4 + 4 + 4 + 4 = 12a + 24 (6 x 2a) + (6 x 4) 6(2a + 4) =

  8. Expanding Brackets Example: 5(2z – 3) Each term inside the brackets is multiplied by the number outside the brackets. Watch out for the signs!

  9. Expanding Brackets Example: 5(2z – 3) (5 x 2z) + 5 x -3

  10. Expanding Brackets Example: 5(2z – 3) (5 x 2z) + 5 x - 3 = 10z – 15

  11. Expanding Brackets Example: 2(3p + 4) + 3(4p + 1)

  12. Expanding Brackets Example: 2(3p + 4) + 3(4p + 1) = (2 x 3p) + (2 x 4)

  13. Expanding Brackets Example: 2(3p + 4) + 3(4p + 1) = (2 x 3p) + (2 x 4) + (3 x 4p) + (3 x 1)

  14. Expanding Brackets Example: 2(3p + 4) + 3(4p + 1) = (2 x 3p) + (2 x 4) + (3 x 4p) + (3 x 1) = 6p + 8

  15. Are you ready for the answers ? 7n - 21 Practice 1:Expand the brackets: (a) (i) 7(n – 3) (ii) 4(2x – 3)   (iii) p(q – 2p) Multiply out: (3) • 5(2y – 3) (1) (c) x(2x +y) (2) 8x -12 pq – 2p² 10y - 15 2x² + xy Lesson

  16. Are you ready for the answers ? 4x + 9 + 3x -21 = 7x - 12 Practice 2:Expand and simplify: (i) 4(x + 5) + 3(x – 7) (2) (ii) 5(3p + 2) – 2(5p – 3) (2) (2) 15p + 10 - 10p + 6 = 5p +16 Lesson

  17. Are you ready for the answers ? By using substitution answer the following questions: (i) Work out the value of 2a + ay when a = 5 and y = –3 (2) (ii) Work out the value of 5t² - 7 when t=4 • Work out the value of 5x + 1 when x = –3 (iv) Work out the value of D when: (4) D = ut + 2kt If u = 5 t = 1.2k = –2 (3) -5 73 -14 1.2 Lesson

  18. Lesson Are you ready for the answers ? x = 11 TOP How much do you know? Solve the following (i) x + 5 = 16 (ii) 3x + 4 = 19 (2) (b) 6y + 9 = 45 (1) (c) 2x – 5 = -1 (2) • 4(x + 3) = 20 (1) • 29 = 9x - 7 (1) (Total 7 marks) x = 5 y = 6 x = 2 x = 2 x = 4

  19. Are you ready for the answers ? x = 4 Practice 1: Solve: (a) (i) 4x + 2 = 18 (ii) 8x – 5 = 19   (iii) 7 = 3y - 8 Multiply out the brackets first: • 2(x + 3) = 16 (1) (c) 3(2x – 3) = 9 (2) x = 3 y = 5 x = 5 x = 3 Lesson

  20. Are you ready for the answers ? x = 4 Practice 2: Solve: (i) 2x + 3 = x + 7 (2) (ii) 8r + 3 = 5r + 12 (2) (iii) 9x – 14 = 4x + 11 (2) (iv) 20y – 16 = 18y - 10 (2) 3r = 9 r = 3 5x = 25 x = 5 2y = 6 y = 3 Lesson

  21. Crossing the equals sign When we take a value across the equals sign we change what it was doing to the opposite. So, if it was + 2 on one side, when we take it to the other it is – 2 If we are x 2 on one side, when we take it to the other it is / 2 For example, x + 5 = 13 x = 13 – 5 x = 8

  22. Using inverse operations to solve equations Solve the following equations using inverse operations. 5x = 45 17 – x = 6 x = 45 ÷ 5 17 = 6 + x 17 – 6 = x x = 9 11 = x We usually write the letter before the equals sign. Check: x = 11 5 × 9 = 45 Check: 17 – 11 = 6

  23. Using inverse operations to solve equations x = 3 7 21 = 3 7 Solve the following equations using inverse operations. 3x – 4 = 14 x = 3 × 7 3x = 14 + 4 3x = 18 x = 21 x = 18 ÷ 3 Check: x = 6 Check: 3 × 6 – 4 = 14

  24. Balancing equations

  25. Constructing an equation Ben and Lucy have the same number of sweets. Ben started with 3 packets of sweets and ate 11 sweets. Lucy started with 2 packets of sweets and ate 3 sweets. How many sweets are there in a packet? Let’s call the number of sweets in a packet, n. We can solve this problem by writing the equation: = 3n– 11 2n– 3 The number of Ben’s sweets is the same as the number of Lucy’s sweets.

  26. Solving the equation Move the unknowns (letter terms) to one side and the numbers to the other Start by writing the equation down. 3n– 11 = 2n– 3 3n - 2n –11 = – 3 3n– 2n = –3 + 11 n= 8 This is the solution. We can check the solution by substituting it back into the original equation: 3  8 – 11 = 2  8 – 3

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