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Master Algebraic Expressions: Remove Brackets, Simplify Terms

Learn to simplify algebraic expressions with like terms, remove brackets, and apply integer rules. Practice examples included.

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Master Algebraic Expressions: Remove Brackets, Simplify Terms

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  1. Algebra Simplifying Algebraic Expressions Removing Brackets Removing Brackets & Simplifying www.mathsrevision.com Evaluating Expressions Factorising – The common factor Created by Mr. Lafferty Maths Dept.

  2. Starter Questions www.mathsrevision.com 2cm 3cm 6cm 2cm Created by Mr. Lafferty Maths Dept.

  3. Algebra Simplifying Algebraic Expressions Learning Intention Success Criteria • To remember the phrase • ‘ like terms.’ • To review tidying up • expressions. • 2. To be able to simplify simple algebraic expressions by collecting ‘ like terms.’ www.mathsrevision.com Created by Mr. Lafferty Maths Dept.

  4. Algebra Simplifying Algebraic Expressions Reminder ! We can only add and subtract “ like terms “ www.mathsrevision.com Created by Mr. Lafferty Maths Dept.

  5. Algebra Simplifying Algebraic Expressions Reminder ! Multiplying terms www.mathsrevision.com ( NOT 2b ) ( NOT 8m ) Created by Mr. Lafferty Maths Dept.

  6. 1 2 3 Algebra Simplifying Algebraic Expressions Question : Find the area of each of the 3 sections of this shape. What is the total area. y www.mathsrevision.com 2 y 2 Created by Mr. Lafferty Maths Dept.

  7. Algebra Simplifying Algebraic Expressions Now try Exercise 1 Ch11 (page 46) www.mathsrevision.com Created by Mr. Lafferty Maths Dept.

  8. 100o 60o Starter Questions 2a 6h www.mathsrevision.com Created by Mr. Lafferty Maths Dept.

  9. Algebra Removing brackets Learning Intention Success Criteria • Understand the key steps in removing brackets. • 1. To explain how to multiply out simply algebraic brackets. • 2. Apply multiplication rules for integers numbers when removing brackets. www.mathsrevision.com Created by Mr. Lafferty Maths Dept.

  10. Removing a Single Bracket Example 1 + 15 3(b + 5) = 3b Example 2 - 8 4(w - 2) = 4w Created by Mr. Lafferty@mathsrevision.com

  11. Removing a Single Bracket Example 3 - 2 2(y - 1) = 2y Example 4 - 42 7(w - 6) = 7w Created by Mr. Lafferty@mathsrevision.com

  12. Removing a Single Bracket Example 5 + 24 8(x + 3) = 8x Example 6 - 8m 4(3 -2m) = 12 Created by Mr. Lafferty@mathsrevision.com

  13. Removing a Single Bracket Example 7 : Write down an expression for the amount indicate below in two difference ways. x+3 x+3 + 9 3(x + 3) =3x x+3 Created by Mr. Lafferty@mathsrevision.com

  14. Removing a Single Bracket Example 8 : Write down an expression for the amount indicate below in two difference ways. y-2 y-2 y-2 - 10 5(y - 2) = 5y y-2 y-2 2-Nov-19 Created by Mr. Lafferty@mathsrevision.com

  15. Algebra Removing brackets Question : Find the area of the rectangle (i) With brackets (ii) Without brackets. 4 www.mathsrevision.com Y + 5 Created by Mr. Lafferty Maths Dept.

  16. Algebra Removing brackets Now try Exercise 2 Ch11 (page 48) www.mathsrevision.com Created by Mr. Lafferty Maths Dept.

  17. Starter Questions www.mathsrevision.com (x+2)cm 7cm Created by Mr. Lafferty Maths Dept.

  18. Algebra Removing Brackets & Simplifying Learning Intention Success Criteria 1. Understand how to remove brackets • 1. Explain how to remove brackets and simplify. 2. Apply rules integer numbers. www.mathsrevision.com 3. Tidy up after removing brackets. Created by Mr. Lafferty Maths Dept.

  19. Removing a Single Bracket Example 1 + 5a a(b + 5) = ab Example 2 - 2p p(w - 2) = pw Created by Mr. Lafferty@mathsrevision.com

  20. Removing a Single Bracket Example 3 - y y(y - 1) = y2 Example 4 - 21w 7w(w - 3) = 7w2 Created by Mr. Lafferty@mathsrevision.com

  21. Removing a Single Bracket Example 5 + 3ab a(a2 + 3b) = a3 Example 6 - 2cy2 y2(3y -2c) = 3y3 Created by Mr. Lafferty@mathsrevision.com

  22. Removing a Single Bracket Example 7 - y -(x + y) = -x Example 8 + 35 -5(a - 7) = -5a Created by Mr. Lafferty@mathsrevision.com

  23. Removing a Single Bracket Tidy Up Example 9 - 3y 12 7 + 3(4 - y) = 7 + = 19 - 3y Tidy Up Example 10 - 24 + 3y 9 - 3(8 - y) = 9 = -15 + 3y Created by Mr. Lafferty@mathsrevision.com

  24. Removing a Single Bracket Example 11 12 10 Find my Area Find my Area x (x - 2) A = L x B A = L x B A = 10(x – 2) A = 12x Created by Mr. Lafferty@mathsrevision.com

  25. Removing a Single Bracket Example 12 : Find area of the orange border 12 Area =Big Rec – Small Rec 10 x (x - 2) = 12x – 10(x - 2) = 12x – 10x + 20 = 2x + 20 Created by Mr. Lafferty@mathsrevision.com

  26. Removing Two Single Brackets Tidy Up Example 13 - m - 2 4(m - 3) - (m + 2) = 4m - 12 = 3m - 14 Tidy Up Example 14 - 2y - 8 7(y - 1) - 2(y + 4) = 7y - 7 = 5y - 15 Created by Mr. Lafferty@mathsrevision.com

  27. Removing Two Single Brackets Example 15 : Find an expression for the difference in the areas. (y - 5) A = 4(y – 5) 7 4 A = 7(y- 4) (y- 4) Calculate difference if y = 14 3 x 14 – 8 = 34 Difference = 7(y - 4) - 4(y – 5) = 7y - 28 - 4y + 20 = 3y - 8 Created by Mr. Lafferty@mathsrevision.com

  28. Removing Two Single Brackets Example 16 : Find an expression for the difference in the areas. (x + 1) A = 7(x + 1) 9 7 A = 9(x + 3) x + 3 Calculate difference if x = 4 2 x 4 + 20 =28 Difference = 9(x + 3) - 7(x + 1) = 9x + 27 – 7x - 7 = 2x + 20 Created by Mr. Lafferty@mathsrevision.com

  29. Algebra Removing Brackets & Simplifying Question : Find the area of the large rectangle, then the small rectangle and hence find the area of the red section. x x-3 4 6 www.mathsrevision.com Created by Mr. Lafferty Maths Dept.

  30. Algebra Removing Brackets & Simplifying Now try Exercise 3 Ch11 (page 50) www.mathsrevision.com Created by Mr. Lafferty Maths Dept.

  31. Starter Questions www.mathsrevision.com (x+2)cm 7cm Created by Mr. Lafferty Maths Dept.

  32. Algebra Evaluating Expressions – number for letter Learning Intention Success Criteria 1. Be able to substitute numbers for letters in an expression. • 1. To show how to evaluate an expression given values for the letters. 2. Use previous knowledge to evaluate expression. www.mathsrevision.com Created by Mr. Lafferty Maths Dept.

  33. Algebra Evaluating Expressions – number for letter BODMAS Given the following information find the values of :- a = 3 ; b = 4 and c = -1 www.mathsrevision.com Created by Mr. Lafferty Maths Dept.

  34. Algebra Evaluating Expressions – number for letter Given the following information find the values of :- a = 3 ; b = 4 and c = -1 www.mathsrevision.com Created by Mr. Lafferty Maths Dept.

  35. Algebra Evaluating Expressions – number for letter Now try Exercise 4 Ch2 (page 51) www.mathsrevision.com Created by Mr. Lafferty Maths Dept.

  36. Starter Questions www.mathsrevision.com Created by Mr. Lafferty Maths Dept.

  37. Algebra Factorising – The Common Factor Learning Intention Success Criteria 1. Be able to recognise the HCF for set of values. • 1. To show how to reverse the process of removing bracket ‘factorising’. 2. Understand the term factorising. www.mathsrevision.com 3. Factorise simple expressions. Created by Mr. Lafferty Maths Dept.

  38. Check by multiplying out the bracket to get back to where you started Factorising S3 Credit Factorise 3x + 15 Example 1. Find the HCF for 3x and 15 3 2. HCF goes outside the bracket 3( ) www.mathsrevision.com • To see what goes inside the bracket • divide each term by HCF 3x ÷ 3 = x 15 ÷ 3 = 5 3( x + 5 ) Created by Mr. Lafferty@www.mathsrevision.com

  39. Check by multiplying out the bracket to get back to where you started Factorising S3 Credit Factorise 4x2 – 6xy Example 1. Find the HCF for 4x2 and 6xy 2x 2. HCF goes outside the bracket 2x( ) www.mathsrevision.com • To see what goes inside the bracket • divide each term by HCF 4x2 ÷ 2x =2x 6xy ÷ 2x = 3y 2x( 2x- 3y ) Created by Mr. Lafferty@www.mathsrevision.com

  40. Algebra Factorising – The Common Factor Simply find the HCF for a given set of data and write the data using brackets :- HCF ? 6 www.mathsrevision.com HCF ? 4 Created by Mr. Lafferty Maths Dept.

  41. Algebra Factorising – The Common Factor Simply find the HCF for a given set of data and write the data using brackets :- HCF ? a www.mathsrevision.com HCF ? 3x Created by Mr. Lafferty Maths Dept.

  42. Factorising S3 Credit Factorise the following : 3(x + 2) • (a) 3x + 6 • 4xy – 2x • 6a + 7a2 • (d) y2 - y Be careful ! 2x(2y – 1) www.mathsrevision.com a(6 + 7a) y(y – 1) Created by Mr. Lafferty@mathsrevision.com

  43. Algebra Factorising – The Common Factor Now try Exercise 5 Ch11 (page 54) www.mathsrevision.com Created by Mr. Lafferty Maths Dept.

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