Algebraic Operations Nat 5 www mathsrevision com Removing
Algebraic Operations Nat 5 www. mathsrevision. com Removing Single Brackets - Revision Removing Double Brackets (ax+b)(cx+d) Alternative Method FOIL – (NOT TAUGHT) Removing Harder Double Brackets Tidying up and Cubing (x+2)3 Solving More equations (x+2)2 =x 2 +64 Exam Questions 04 -Nov-20 Created by Mr. Lafferty@mathsrevision. com
Starter Questions Nat 5 www. mathsrevision. com Q 1. Is the following true or false (a) (-3 a) x 5 a = -15 a (a) (-6 x) x (-7 y) =-42 xy Q 2. Are the 2 answers the same ? (a) (-3 h)2 = (b) -(3 d)2 = Q 3. Spilt £ 64 pounds into the ratio 7: 9 Q 4. Explain why 0. 0675 is equal to 6. 75 x 10 -2 04 -Nov-20 Created by Mr. Lafferty@mathsrevision. com
Removing a Single Bracket www. mathsrevision. com Nat 5 Learning Intention 1. We are learning how to multiply out (remove) various single brackets. 04 -Nov-20 Success Criteria 1. Understand the keypoints of multiplying out an expression with a single bracket. Created by Mr. Lafferty@mathsrevision. com
Removing a Single Bracket Nat 5 www. mathsrevision. com Example 1 3(b + 5) = 3 b + 15 Example 2 4(w - 2) = 4 w - 8 04 -Nov-20 Created by Mr. Lafferty@mathsrevision. com
Removing a Single Bracket Nat 5 www. mathsrevision. com Example 3 : Write down an expression for the amount indicate below in two difference ways. x+3 3(x + 3) =3 x + 9 x+3 04 -Nov-20 Created by Mr. Lafferty@mathsrevision. com
Removing a Single Bracket Nat 5 www. mathsrevision. com Example 8 : Write down an expression for the amount indicate below in two difference ways. y-2 y-2 04 -Nov-20 y-2 5(y - 2) = 5 y - 10 y-2 Created by Mr. Lafferty@mathsrevision. com
Removing a Single Bracket Nat 5 www. mathsrevision. com Example 4 a(b + 5) = ab + 5 a Example 5 p(w - 2) = pw - 2 p 04 -Nov-20 Created by Mr. Lafferty@mathsrevision. com
Removing a Single Bracket Nat 5 www. mathsrevision. com Example 6 y(y - 1) = y 2 - y Example 7 7 w(w - 3) = 7 w 2 - 21 w 04 -Nov-20 Created by Mr. Lafferty@mathsrevision. com
Removing a Single Bracket Nat 5 www. mathsrevision. com Example 8 -(x + y) = -x - y Example 9 -5(a - 7) = -5 a + 35 04 -Nov-20 Created by Mr. Lafferty@mathsrevision. com
Removing a Single Bracket Nat 5 www. mathsrevision. com Example 10 Tidy Up 7 + 3(4 - y) = 7 + 12 - 3 y = 19 - 3 y Tidy Up Example 11 04 -Nov-20 9 - 3(8 - y) = 9 - 24 + 3 y = -15 + 3 y Created by Mr. Lafferty@mathsrevision. com
Removing Two Single Brackets Nat 5 Tidy Up www. mathsrevision. com Example 12 4(m - 3) - (m + 2) = 4 m - 12 - m - 2 = 3 m - 14 Tidy Up Example 13 7(y - 1) - 2(y + 4) = 7 y - 7 - 2 y - 8 = 5 y - 15 04 -Nov-20 Created by Mr. Lafferty@mathsrevision. com
Removing a Single Bracket www. mathsrevision. com Nat 5 Now try Ex 1. 1 Ch 1 N 5 TJ (page 13) 04 -Nov-20 Created by Mr. Lafferty@mathsrevision. com
Starter Questions Nat 5 www. mathsrevision. com Q 1. Find the area of the shape given (w – 5) 3 Q 2. Is the following true -2 a( b – a) = -2 ab +4 a Q 3. Write down the two numbers that multiply to give 8 and subtract to give 2. 04 -Nov-20 Created by Mr. Lafferty@mathsrevision. com
Removing Double Brackets www. mathsrevision. com Int 2 Learning Intention 1. We are learning how to multiply out a pair of brackets using the multiplication table method. 04 -Nov-20 Success Criteria 1. Understand the keypoints of multiplying out paired brackets. 2. Be able to multiply out paired brackets using the multiplication table method. Created by Mr. Lafferty@mathsrevision. com
What is the total Removing area of the Double Brackets downstairs house? Nat 5 www. mathsrevision. com Below is a floor plan of the down stairs of a house. y 5 y Living 2 Room y Bedroom 3 Bathroom 3 y Kitchen 04 -Nov-20 5 y 15 Created by Mr. Lafferty@mathsrevision. com Tidy up ! y 2 + 8 y + 15
Removing Double Brackets Double Nat 5 www. mathsrevision. com Multiplication table for Example 1 brackets are brackets used in AREA calculations (y y + 3)(y 3 y + 5) 5 y 2 +5 y +3 y +15 04 -Nov-20 Created by Mr. Lafferty@mathsrevision. com Tidy up ! y 2 + 8 y + 15
Removing Double Brackets. Be careful Nat 5 with the negative signs Example 2 www. mathsrevision. com (2 x 2 x - 1)(x 1 x + 3) 3 04 -Nov-20 2 x 2 +6 x -x -3 Tidy up ! 2 x 2 + 5 x - 3 Created by Mr. Lafferty@mathsrevision. com
Squaring Brackets Nat 5 www. mathsrevision. com Example 3 : (x + 1)2 = (x + 1) Multiply out the brackets and Simplify (x x + 1)(x 1 x + 1) 1 x 2 + x +x +1 04 -Nov-20 Tidy up ! x 2 + 2 x + 1 Created by Mr. Lafferty@mathsrevision. com
Harder Brackets Nat 5 www. mathsrevision. com Example 4 : Find the area of the square. (2 x 2 x - 3 y 3 y) (2 x-3 y) 4 x 2 -6 xy +9 y 2 04 -Nov-20 Tidy up ! 4 x 2 - 12 xy + 9 y 2 Created by Mr. Lafferty@mathsrevision. com
Harder Double Brackets Just a bigger Nat 5 Multiplication Table www. mathsrevision. com Example 5 (x 4 x 2 + 3 x + 2 2) x + 4)(x 04 -Nov-20 x 3 +3 x 2 +2 x +4 x 2 +12 x +8 Tidy up ! x 3 + 7 x 2 + 14 x + 8 Created by Mr. Lafferty@mathsrevision. com
Removing Double Brackets Just a bigger Nat 5 Multiplication Table www. mathsrevision. com Example 6 (2 x 1 x 2 + 2 x - 1) 1 2 x - 1)(x 04 -Nov-20 2 x 3 +4 x 2 -2 x -x 2 -2 x +1 Tidy up ! 2 x 3 + 3 x 2 - 4 x + 1 Created by Mr. Lafferty@mathsrevision. com
Harder Brackets www. mathsrevision. com 1 2 a 2 a ( ( 4 a 2 -1 -1 04 -Nov-20 2 1 2 a 2 a ( Example 7 : 1 2 a 2 a ( Nat 5 Tidy up ! 1 4 a 2 Created by Mr. Lafferty@mathsrevision. com 1 4 a 2 - 2 + 4 a 2
Removing a Single Bracket www. mathsrevision. com Nat 5 Now try Ex 1. 2 Ch 1 N 5 TJ (page 14) 04 -Nov-20 Created by Mr. Lafferty@mathsrevision. com
Starter Questions www. mathsrevision. com Nat 5 Q 1. 0. 00897 is in scientific notation is this statement True or False? Q 2. Does (w + 2)(w + 1) = w 2 + 3 w + 2 Q 3. 04 -Nov-20 Created by Mr. Lafferty@mathsrevision. com
Removing Double Brackets www. mathsrevision. com Int 2 Learning Intention 1. We are learning how to multiply out a pair of brackets using FOIL. Success Criteria 1. Understand the keypoints of multiplying out double brackets using FOIL. 2. Be able to multiply out double brackets using FOIL. 04 -Nov-20 Created by Mr. Lafferty@mathsrevision. com
Removing a Single Bracket www. mathsrevision. com Nat 5 Now try Ex 1. 3 Ch 1 N 5 TJ (page 17) 04 -Nov-20 Created by Mr. Lafferty@mathsrevision. com
Removing Double Brackets www. mathsrevision. com Nat 5 We can use the F O I L method to multiply out DOUBLE brackets. FOIL Method Simply remember the word FOIL Multiply First 2 Multiply Outside 2 04 -Nov-20 Created by Mr. Lafferty@mathsrevision. com Multiply Last 2 Multiply Inside 2
Removing Try again using multiplication Double Bracketstable www. mathsrevision. com Nat 5 Example 1 : Multiply out the brackets and Simplify (x + 1)(x + 2) 1. Write down 2. Tidy up ! 04 -Nov-20 F O I L x 2 + 2 x + 2 x 2 + 3 x + 2 Created by Mr. Lafferty@mathsrevision. com
Removing Try again using multiplication Double Bracketstable www. mathsrevision. com Nat 5 Example 2 : Multiply out the brackets and Simplify (x - 1)(x + 2) 1. Write down 2. Tidy up ! 04 -Nov-20 F O I L x 2 + 2 x - 2 x 2 + x - 2 Created by Mr. Lafferty@mathsrevision. com
Squaring Brackets www. mathsrevision. com Nat 5 FOIL method is very limited therefore from now on we will use the multiplication table method. 04 -Nov-20 Created by Mr. Lafferty@mathsrevision. com
Removing Double Brackets www. mathsrevision. com Nat 5 (x + 1)(x - 2) x 2 - x - 2 (x - 1)(x - 2) x 2 - 3 x + 2 (x + 3)(x + 2) x 2 + 5 x + 6 (x - 3)(x + 2) x 2 - x - 6 (x + 3)(x - 2) x 2 + x - 6 04 -Nov-20 Created by Mr. Lafferty@mathsrevision. com
Removing a Single Bracket www. mathsrevision. com Nat 5 Now try Ex 1. 2 Ch 1 N 5 TJ (page 14) 04 -Nov-20 Created by Mr. Lafferty@mathsrevision. com
Starter Questions Nat 5 www. mathsrevision. com Q 1. Does (x - 4)2 = x 2 + 8 x + 16 Q 2. 3 + (-4) x 5 Q 3. Is it true 04 -Nov-20 Created by Mr. Lafferty@mathsrevision. com
Simplifying Expressions www. mathsrevision. com Nat 5 Learning Intention 1. We are learning how to expand tidy up complicated expressions that include squared and cubed brackets. 04 -Nov-20 Success Criteria 1. Use techniques learned so far to simplify complicated brackets. Created by Mr. Lafferty@mathsrevision. com
YOUExpressions need to be Simplifying multiplication table VERYUse CAREFUL !! to remove brackets. Nat 5 www. mathsrevision. com Example 1 (2 m - 3)(3 m + 1) – (m - 1)2 6 m 2 - 7 m - 3 - ( m 2 – 2 m + 1 ) 6 m 2 - 7 m - 3 - m 2 + 2 m – 1 Tidy up 04 -Nov-20 5 m 2 – 5 m - 4 Created by Mr. Lafferty@mathsrevision. com
Nat 5 Simplifying Expressions Use multiplication table for first two brackets. www. mathsrevision. com Example 1 (5 y – 2)3 (5 y – 2)(5 y – 2) Use multiplication table again (25 y 2 – 20 y + 4) ( 5 y – 2) 125 y 3 – 150 y 2 + 60 y - 8 04 -Nov-20 Created by Mr. Lafferty@mathsrevision. com
Simplifying Expressions www. mathsrevision. com Nat 5 Now try Ex 1. 3 Ch 1 N 5 TJ (page 17) 04 -Nov-20 Created by Mr. Lafferty@mathsrevision. com
Starter Questions Nat 5 www. mathsrevision. com Q 1. Does (x + 3)2 = x 2 + 9 Q 2. The sun is 92 million mile away from the earth. Write this in standard form. Q 3. Is it true 04 -Nov-20 Created by Mr. Lafferty@mathsrevision. com
Equations and brackets www. mathsrevision. com Nat 5 Learning Intention 1. We are learning how to solve equations that have paired or squared brackets. 04 -Nov-20 Success Criteria 1. Be able to solve equations that contain paired or squared brackets using multiplication table and balancing method. Created by Mr. Lafferty@mathsrevision. com
Equations and brackets Multiplication Nat 5 table www. mathsrevision. com Example 1 Balancing Method 12 12 m(m + 4) = (m + 1)(m+2) m 2 + 4 m = m 2 + 3 m + 2 4 m = 3 m + 2 Check ! 04 -Nov-20 m =2 Created by Mr. Lafferty@mathsrevision. com
Equations and brackets Multiplication www. mathsrevision. com Nat 5 table 25 25 Example 2 Balancing Method 04 -Nov-20 (x + 5)2 = (x - 5)2 (x + 5) = (x - 5) x 2 + 10 x + 25 = x 2 – 10 x + 25 = -10 x + 25 20 x = 0 20 20 Check ! x =0 Created by Mr. Lafferty@mathsrevision. com
Equations and brackets Nat 5 www. mathsrevision. com Example 3 : The two areas are equal. Find the value of x. (x + 2) A = (x + 7)(x – 2) 2)2 400 (x + 7) 400 (x + 2)2 = (x + 7)(x - 2) x 2 + 4 x + 4 = x 2 + 5 x - 14 Swap ! 4 x + 4 = 5 x - 14 = 4 x + 4 Check ! x = 18 04 -Nov-20 Created by Mr. Lafferty@mathsrevision. com Multiplication table Balancing Method
Equations and Brackets www. mathsrevision. com Nat 5 Now try Ex 1. 4 Ch 1 N 5 TJ (page 18) 04 -Nov-20 Created by Mr. Lafferty@mathsrevision. com
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