S3.3 Algebraic Operations Removing Brackets of the type 2(x-1) Pair of brackets (x+3)(x+4) Removing Brackets of the type y(3+a) Removing Brackets of the type -2(x+1) Equations and brackets 3(x-4) = 2(x-1) More equations (x+2) 2 =x May-15Created by Mr. Squaring Brackets (x+4) 2

4-May-15 Starter Questions Q1.Is the following true or false (a)(-3a) x 5a = -15a (a) (-6x) x (-7y) =-42xy Q2.Are the 2 answers the same ? (a)(-3h) 2 =(b)-(3d) 2 = S3.3 Created by Mr. Q3.Spilt £64 pounds into the ratio 7:9 Q4.Explain why is equal to 6.75 x 10 -2

4-May-15 Learning Intention Success Criteria 1.To show how to multiply out (remove) a single bracket with a positive number outside the bracket. 1.Understand the keypoints of multiplying out an expression with a single bracket and a positive number outside the bracket. S3.3 2.Be able multiply out a expression with a single bracket. Created by Mr. Removing a Single Bracket

4-May-15Created by Mr. Lafferty Maths Dept. Algebra Simplifying Algebraic Expressions Reminder ! We can only add and subtract “ like terms “

4-May-15Created by Mr. Lafferty Maths Dept. Algebra Simplifying Algebraic Expressions Reminder ! Multiplying terms ( NOT 2b ) ( NOT 8m )

S3.3 3(b + 5) =3b + 15 Example 1 4(w - 2) =4w - 8 Example 2 4-May-15Created by Mr. Removing a Single Bracket

S3.3 2(y - 1) =2y - 2 Example 3 7(w - 6) =7w - 42 Example 4 4-May-15Created by Mr. Removing a Single Bracket

S3.3 8(x + 3) =8x + 24 Example 5 4(3 -2m) =12 - 8m Example 6 4-May-15Created by Mr. Removing a Single Bracket

S3.3 Example 7 : Write down an expression for the amount indicate below in two difference ways. 3(x + 3)=3x May-15Created by Mr. Removing a Single Bracket x+3

S3.3 Example 8 : Write down an expression for the amount indicate below in two difference ways. 5(y - 2)= 5y May-15 Created by Mr. Removing a Single Bracket y-2

4-May-15Created by Mr. Now try Ex 2.1 Ch3 MIA (page 43) S3.3 Removing a Single Bracket

4-May-15 Starter Questions Q1. Explain why the following are True or False (a)-3y x 5y =-30y (b)-6q x (-4q) = 24q 2 Q2. Is the following true -2a( b – a) = -2ab +4a S3.3 Created by Mr. Q3.Write down the two numbers that multiply to give 8 and subtract to give 2.

4-May-15 Learning Intention Success Criteria 1.To show how to multiply out (remove) a single bracket with a letter outside the bracket. 1.Understand the keypoints of multiplying out an expression with a single bracket with a letter outside. S3.3 2.Be able multiply out a expression with a single bracket with a letter outside the bracket. Created by Mr. Removing a Single Bracket

S3.3 a(b + 5) =ab + 5a Example 1 p(w - 2) =pw - 2p Example 2 4-May-15Created by Mr. Removing a Single Bracket

S3.3 y(y - 1) =y2y2 - y Example 3 7w(w - 3) =7w w Example 4 4-May-15Created by Mr. Removing a Single Bracket

S3.3 a(a 2 + 3b) =a3a3 + 3ab Example 5 y 2 (3y -2c) =3y 3 - 2cy 2 Example 6 4-May-15Created by Mr. Removing a Single Bracket

4-May-15Created by Mr. Now try Ex 2.2 Ch3 MIA (page 44) S3.3 Removing a Single Bracket

4-May-15 Starter Questions Q1.Multiply out. (a)3y(x - y) =(b)6q 2 (2 - 4q) = Q2.Explain your working to show that if we split 24 into the ratio 1:5 the answer is 4:20 S3.3 Created by Mr. Q3.Writing out in full 5.2 x to get Is the correct?

4-May-15 Learning Intention Success Criteria 1.To show how to multiply out (remove) a single bracket with a negative outside the bracket. 1.Understand the keypoints of multiplying out an expression with a single bracket with a negative outside. S3.3 2.Be able multiply out a expression with a single bracket with a negative outside the bracket. Created by Mr. Removing a Single Bracket

S3.3 -(x + y) =-x - y Example 1 -5(a - 7) =-5a + 35 Example 2 4-May-15Created by Mr. Removing a Single Bracket

S (4 - y) = Example (8 - y) = Example 4 4-May-15Created by Mr. Removing a Single Bracket - 3y = y Tidy Up + 3y Tidy Up = y

S3.3 A = 10(x – 2) Example 9 4-May-15Created by Mr. Removing a Single Bracket Find my Area (x - 2) 10 Find my Area x 12 A = 12x A = L x BA = L x B

S3.3 Example 9 : Find area of the orange border 4-May-15Created by Mr. Removing a Single Bracket (x - 2) 10 x 12 Area =Big Rec – Small Rec = 12x – 10(x - 2) = 12x – 10x + 20 = 2x + 20

4-May-15Created by Mr. Now try Ex 3.1 Ch3 MIA (page 44) S3.3 Removing a Single Bracket

4-May-15 Starter Questions Q1.Find the area of the second shape given the first has area 7w - 14 Q2.Split 48 into the ratio 1:3 S3.3 Created by Mr. Q3.In standard form is 1.8x10 7 is the correct? (w - 2) 7 (w – 5) 3

4-May-15 Learning Intention Success Criteria 1.To show how to multiply out (remove) and simplify an expression that has two single brackets. 1.Understand the keypoints of multiplying out an expression with two single brackets. S3.3 2.Be able multiply out a expression with two single brackets and the simplify. Created by Mr. Removing Two Single Brackets

S3.3 4(m - 3) - (m + 2) =4m m - 2 Example 1 Example 2 4-May-15Created by Mr. = 3m - 14 Tidy Up 7(y - 1) - 2(y + 4) =7y y - 8 = 5y - 15 Tidy Up Removing Two Single Brackets

S3.3 3 x 14 – 8 = 34 A = 4(y – 5) Example 3 : Find an expression for the difference in the areas. 4-May-15Created by Mr. (y - 5) 47 A = 7(y- 4) (y- 4) Difference = 7(y - 4) - 4(y – 5) = 7y y + 20 = 3y - 8 Calculate difference if y = 14 Removing Two Single Brackets

S3.3 2 x =28 A = 7(x + 1) Example 3 : Find an expression for the difference in the areas. 4-May-15Created by Mr. (x + 1) 79 A = 9(x + 3) x + 3 Difference = 9(x + 3) - 7(x + 1) = 9x + 27 – 7x - 7 = 2x + 20 Calculate difference if x = 4 Removing Two Single Brackets

4-May-15Created by Mr. Now try Ex 3.2 Ch3 MIA (page 46) S3.3 Removing Two Single Brackets

4-May-15 Starter Questions Q1.Solve for x (a)x + 3 = 8(b)2x – 14 = 50 Q2.Is this statement true (x – 1) – 3(x + 1) = -2x S3.3 Created by Mr. Q3.

4-May-15 Learning Intention Success Criteria 1.To show how to solve equations that have bracket terms. 1.Be able to multiply out brackets and solve equations. S3.3 Created by Mr. Equations and brackets

S3.3 5(x - 3) = 25 5x Example 1 4-May-15Created by Mr = 25 Multiply out the bracket first and then solve. Equations and brackets 5x = x = 40 ÷ 5 = 40 = 8

S3.3 6(x - 2) = 3(x + 1) 6x Example 2 4-May-15Created by Mr = 3x Equations and brackets = x – 3x -12 3x -12 = 3 3x = = 15 x = 15 ÷ (3) = 5 Solve as normal Substitute value into original equation to check answer 18

S3.3 -3(2 + 2y) = 6 – (y + 2) -6 Example 3 4-May-15Created by Mr. - 6y = 6 Equations and brackets = 4 - y - y – 6y y + y = 4 -6 – 5y = 4 – 5y = 10 y = 10 ÷ (-5) = -2 Tidy up RHS Solve as normal Substitute value into original equation to check answer 6 6

4-May-15Created by Mr. Now try Ex 4.1 & Ex 4.2 Ch3 MIA (page 47) S3.3 Equations and brackets

4-May-15 Starter Questions Q1.Does = 5.793x10 5 Q2.Explain why the answer to 4(w + 2) = 6(w + 1) is w = 1 S3.3 Created by Mr. Q3.

4-May-15 Learning Intention Success Criteria 1.To show how to multiply out a pair of brackets using a multiplication table. 1.Understand the keypoints of multiplying out paired brackets. Int 2 2.Be able to multiply out paired brackets using a multiplication table. Created by Mr. Removing Double Brackets

S3.3 Below is a floor plan of the down stairs of a house. 4-May-15Created by Mr. Removing Double Brackets y 5 y 3 Tidy up ! y 2 + 8y + 15 Living Room Kitchen Bathroom Bedroom What is the total area of the downstairs house? y 2 5y 3y15

S3.3 Multiplication table for brackets 4-May-15Created by Mr. Removing Double Brackets (y + 3)(y + 5)y+ 3y+ 5 Double brackets are used in AREA calculations +5y +15+3y y 2 Tidy up ! y 2 + 8y + 15

S3.3 Example 2 4-May-15Created by Mr. Removing Double Brackets (2x - 1)(x + 3)2x- 1x+ 3 Be careful with the negative signs +6x -3 -x 2x 2 Tidy up ! 2x 2 + 5x - 3

S3.3 Example 3 4-May-15Created by Mr. Removing Double Brackets (x + 4)(x 2 + 3x + 2) x+ 4 x2x2 + 3x Just a bigger Multiplication Table +3x 2 +12x +4x 2 x 3 Tidy up ! x x x x+ 8

4-May-15Created by Mr. Now try Ex 5.1 First column in each Question Ch3 MIA (page 49) S3.3 Removing Double Bracket

4-May-15 Starter Questions Q is in scientific notation is this statement True or False? Q2.Why does (w + 2)(w + 1) = w 2 + 3w + 2 S3.3 Created by Mr. Q3.

4-May-15 Learning Intention Success Criteria 1.To show how to multiply out a pair of brackets using FOIL. 1.Understand the keypoints of multiplying out double brackets using FOIL. Int 2 2.Be able to multiply out double brackets using FOIL. Created by Mr. Removing Double Brackets

S3.3 We can use the F O I L method to multiply out DOUBLE brackets. 4-May-15Created by Mr. Removing Double Brackets Simply remember the word FOIL Multiply First 2 Multiply Last 2 Multiply Outside 2 Multiply Inside 2 FOIL Method

S3.3 (x + 1)(x + 2) x2x2 + 2x Example 1 : Multiply out the brackets and Simplify 4-May-15Created by Mr. 1.Write down F O I L + x Tidy up ! x 2 + 3x + 2 Removing Double Brackets Try again using multiplication table

S3.3 (x - 1)(x + 2) x2x2 + 2x Example 2 : Multiply out the brackets and Simplify 4-May-15Created by Mr. Removing Double Brackets 1.Write down F O I L - x Tidy up ! x 2 + x - 2 Try again using multiplication table

S3.3 FOIL method is very limited therefore from now on we will use the multiplication table method. 4-May-15Created by Mr. Squaring Brackets

S3.3 4-May-15Created by Mr. (x + 1)(x - 2) Removing Double Brackets (x - 1)(x - 2) (x + 3)(x + 2) (x - 3)(x + 2) (x + 3)(x - 2) x 2 - x - 2 x 2 - 3x + 2 x 2 + 5x + 6 x 2 - x - 6 x 2 + x - 6

4-May-15Created by Mr. Now try Ex 5.2 First column in each Question Ch3 MIA (page 50) S3.3 Removing Double Brackets

4-May-15 Starter Questions Q1.Does x 4 = 20 Explain ? Q2.Multiply out using a multiplication table (w + 2)(w 2 - 2w + 1) S3.3 Created by Mr. Q3.Which sums are true

4-May-15 Learning Intention Success Criteria 1.To show how to multiply out squared brackets using Multiplication Table. 1.Understand the keypoints of multiplying out squared brackets using. 1.Understand the keypoints of multiplying out squared brackets using Multiplication Table. Int 2 2.Be able to multiply out squared brackets using. 2.Be able to multiply out squared brackets using Multiplication Table. Created by Mr. Squaring Brackets

S3.3 = (x + 1)(x + 1) Example 1 : (x + 1) 2 Multiply out the brackets and Simplify 4-May-15Created by Mr. Squaring Brackets (x + 1)(x + 1)x+ 1x+ 1 + x + 1+ x x 2 Tidy up ! x 2 + 2x + 1

S3.3 Example 2 : (x + y) 2 Multiply out the brackets and Simplify 4-May-15Created by Mr. Squaring Brackets = (x + y)(x + y) (x + y)(x + y)x+ yx+ y +xy + y 2 +xy x 2 Tidy up ! x 2 + 2xy +y 2

S3.3 4-May-15Created by Mr. (x - 1) 2 (x - 2) 2 (x - 4) 2 (2x – 1) x 2 - 2x + 1 x 2 - 4x + 4 x 2 - 8x x 2 - 4x + 1 Squaring Brackets

4-May-15Created by Mr. Now try Ex 6.1 & 6.2 First column in each Question Ch3 MIA (page 50) S3.3 Squaring Brackets

4-May-15 Starter Questions Q1.Does (x + 3) 2 = x Q2.The sun is 92 million mile away from the earth. Write this in standard form. S3.3 Created by Mr. Q3.Is it true

4-May-15 Learning Intention Success Criteria 1.To show how to solve equations that have paired or squared brackets. 1.Be able to solve equations that contain paired or squared brackets. S3.3 Created by Mr. Equations and brackets

S3.3 (x + 2) 2 = x (x + 2)(x + 2) Example 1 4-May-15Created by Mr. = x Multiply out the bracket first and then solve. Equations and brackets x 2 + 4x + 4 4x = 60 x = 60 ÷ 4 = 15 X table = x x + 4 = 64 Substitute value into original equation to check answer 289

S3.3 m(m + 2) = m m 2 + 2m Example 2 4-May-15Created by Mr. = m Multiply out the bracket first and then solve. Equations and brackets 2m m = 10 ÷ 2 = 5 = 10 Substitute value into original equation to check answer 35

S3.3 6(x - 2) = 3(x + 1) 6x Example 3 4-May-15Created by Mr = 3x Equations and brackets = x – 3x -12 3x -12 = 3 3x = = 15 x = 15 ÷ (3) = 5 Solve as normal Substitute value into original equation to check answer 18

S3.3 -3(2 + 2y) = 6 – (y + 2) -6 Example 4 4-May-15Created by Mr. - 6y = 6 Equations and brackets = 4 - y - y – 6y y + y = 4 -6 – 5y = 4 – 5y = 10 y = 10 ÷ (-5) = -2 Tidy up RHS Solve as normal Substitute value into original equation to check answer 6 6

S3.3 Solve in the usual way A = (x + 7)(x – 2) Example 5 : The two areas are equal. Find the value of x. 4-May-15Created by Mr. (x + 7) (x – 2) (x + 2) A = (x + 2) 2 (x + 2) 2 = (x + 7) (x - 2) x 2 + 4x + 4 x = 18 X table Equations and brackets = x 2 + 5x x + 4= 5x = x - 14 Substitute value into original equation to check answer 400

4-May-15Created by Mr. Now try Ex 7.1 & 7.2 Ch3 MIA (page 55) S3.3 Equations and brackets