Nat 5 Algebraic Operations Removing Single Brackets - Revision Removing Double Brackets (ax+b)(cx+d) Alternative Method FOIL – ( NOT TAUGHT) Solving More equations (x+2) 2 =x Nov-15Created by Mr. Removing Harder Double Brackets Tidying up and Cubing (x+2) 3 Exam Questions

12-Nov-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 = Nat 5 Created by Mr. Q3.Spilt £64 pounds into the ratio 7:9 Q4.Explain why is equal to 6.75 x 10 -2

12-Nov-15 Learning Intention Success Criteria 1.We are learning how to multiply out (remove) various single brackets. 1.Understand the keypoints of multiplying out an expression with a single bracket. Nat 5 Created by Mr. Removing a Single Bracket

Nat 5 3(b + 5) =3b + 15 Example 1 4(w - 2) =4w - 8 Example 2 12-Nov-15Created by Mr. Removing a Single Bracket

Nat 5 Example 3 : Write down an expression for the amount indicate below in two difference ways. 3(x + 3)=3x Nov-15Created by Mr. Removing a Single Bracket x+3

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

Nat 5 a(b + 5) =ab + 5a Example 4 p(w - 2) =pw - 2p Example 5 12-Nov-15Created by Mr. Removing a Single Bracket

Nat 5 y(y - 1) =y2y2 - y Example 6 7w(w - 3) =7w w Example 7 12-Nov-15Created by Mr. Removing a Single Bracket

Nat 5 -(x + y) =-x - y Example 8 -5(a - 7) =-5a + 35 Example 9 12-Nov-15Created by Mr. Removing a Single Bracket

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

Nat 5 4(m - 3) - (m + 2) =4m m - 2 Example 12 Example Nov-15Created by Mr. = 3m - 14 Tidy Up 7(y - 1) - 2(y + 4) =7y y - 8 = 5y - 15 Tidy Up Removing Two Single Brackets

12-Nov-15Created by Mr. Now try Ex 1.1 Ch1 N5 TJ (page 13) Nat 5 Removing a Single Bracket

12-Nov-15 Starter Questions Q1.Find the area of the shape given Nat 5 Created by Mr. (w – 5) 3 Q2. Is the following true -2a( b – a) = -2ab +4a Q3.Write down the two numbers that multiply to give 8 and subtract to give 2.

12-Nov-15 Learning Intention Success Criteria 1.We are learning how to multiply out a pair of brackets using the multiplication table method. 1.Understand the keypoints of multiplying out paired brackets. Int 2 2.Be able to multiply out paired brackets using the multiplication table method. Created by Mr. Removing Double Brackets

Nat 5 Below is a floor plan of the down stairs of a house. 12-Nov-15Created by Mr. Removing Double Brackets y 5 y 3 y 2 + 8y + 15 Living Room Kitchen Bathroom Bedroom What is the total area of the downstairs house? y 2 5y 3y15 Tidy up !

Nat 5 Multiplication table for brackets 12-Nov-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 y 2 + 8y + 15 Example 1 Tidy up !

Nat 5 Example 2 12-Nov-15Created by Mr. Removing Double Brackets (2x - 1)(x + 3)2x- 1x+ 3 Be careful with the negative signs +6x -3 -x 2x 2 2x 2 + 5x - 3 Tidy up !

Nat 5 = (x + 1)(x + 1) Example 3 : (x + 1) 2 Multiply out the brackets and Simplify 12-Nov-15Created by Mr. Squaring Brackets (x + 1)(x + 1)x+ 1x+ 1 + x + 1+ x x 2 x 2 + 2x + 1 Tidy up !

Nat 5 Example 4 : Find the area of the square. 12-Nov-15Created by Mr. Harder Brackets (2x - 3y)(2x - 3y)2x- 3y2x- 3y -6xy +9y 2 -6xy 4x 2 4x xy + 9y 2 (2x-3y) Tidy up !

Nat 5 Example 5 12-Nov-15Created by Mr. Harder Double Brackets (x + 4)(x 2 + 3x + 2) x + 4x2x2 + 3x Just a bigger Multiplication Table +3x 2 +12x +4x 2 x 3 x x x x+ 8 Tidy up !

Nat 5 Example 6 12-Nov-15Created by Mr. Removing Double Brackets (2 - 1)(x 2 + 2x - 1) 2x - 1x2x2 + 2x Just a bigger Multiplication Table +4x 2 -2x -x 2 2x 3 2x x x 2 - 4x+ 1 Tidy up !

Nat 5 Example 7 : 12-Nov-15Created by Mr. Harder Brackets a 2 2a ( ( ( ( 1 - ( ( a 2 4a Tidy up !

12-Nov-15Created by Mr. Now try Ex 1.2 Ch1 N5 TJ (page 14) Nat 5 Removing a Single Bracket

12-Nov-15 Starter Questions Q is in scientific notation is this statement True or False? Q2.Does (w + 2)(w + 1) = w 2 + 3w + 2 Nat 5 Created by Mr. Q3.

12-Nov-15 Learning Intention Success Criteria 1.We are learning 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

12-Nov-15Created by Mr. Now try Ex 1.3 Ch1 N5 TJ (page 17) Nat 5 Removing a Single Bracket

Nat 5 We can use the F O I L method to multiply out DOUBLE brackets. 12-Nov-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

Nat 5 (x + 1)(x + 2) x2x2 + 2x Example 1 : Multiply out the brackets and Simplify 12-Nov-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

Nat 5 (x - 1)(x + 2) x2x2 + 2x Example 2 : Multiply out the brackets and Simplify 12-Nov-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

Nat 5 FOIL method is very limited therefore from now on we will use the multiplication table method. 12-Nov-15Created by Mr. Squaring Brackets

Nat 5 12-Nov-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

12-Nov-15Created by Mr. Now try Ex 1.2 Ch1 N5 TJ (page 14) Nat 5 Removing a Single Bracket

12-Nov-15 Starter Questions Q1.Does (x - 4) 2 = x 2 + 8x + 16 Q2.3 + (-4) x 5 Nat 5 Created by Mr. Q3.Is it true

12-Nov-15 Learning Intention Success Criteria 1.We are learning how to expand and tidy up complicated expressions that include squared and cubed brackets. 1.Use techniques learned so far to simplify complicated brackets. Nat 5 Created by Mr. Simplifying Expressions

Nat 5 6m 2 - 7m - 3 Example 1 12-Nov-15Created by Mr. ( m 2 – 2m + 1 ) Simplifying Expressions Use multiplication table to remove brackets. Tidy up - 6m 2 - 7m m 2 + 2m – 1 5m 2 – 5m - 4 YOU need to be VERY CAREFUL !! (2m - 3)(3m + 1) – (m - 1) 2

Nat 5 (5y – 2) 3 (25y 2 – 20y + 4) Example 1 12-Nov-15Created by Mr. ( 5y – 2) Simplifying Expressions Use multiplication table for first two brackets. 125y 3 – 150y y - 8 (5y – 2)(5y – 2)(5y – 2) Use multiplication table again

12-Nov-15Created by Mr. Now try Ex 1.3 Ch1 N5 TJ (page 17) Nat 5 Simplifying Expressions

12-Nov-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. Nat 5 Created by Mr. Q3.Is it true

12-Nov-15 Learning Intention Success Criteria 1.We are learning how to solve equations that have paired or squared brackets. 1.Be able to solve equations that contain paired or squared brackets using multiplication table and balancing method. Nat 5 Created by Mr. Equations and brackets

Nat 5 m(m + 4) = (m + 1)(m+2) m 2 + 4m Example 1 12-Nov-15Created by Mr. = m 2 + 3m + 2 Equations and brackets 4m m = 2 = 3m Multiplication table Balancing Method Check !

Nat 5 (x + 5) 2 = (x - 5) 2 (x + 5)(x + 5) Example 2 12-Nov-15Created by Mr. = (x - 5)(x - 5) Equations and brackets x x x = 0 x = 0 Multiplication table = x 2 – 10x x + 25 = -10x + 25 Balancing Method 25 Check !

Nat 5 Balancing Method A = (x + 7)(x – 2) Example 3 : The two areas are equal. Find the value of x. 12-Nov-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 Multiplication table Equations and brackets = x 2 + 5x x + 4= 5x = x Check !

12-Nov-15Created by Mr. Now try Ex 1.4 Ch1 N5 TJ (page 18) Nat 5 Equations and Brackets