algebraic operations
DESCRIPTION
Algebraic Operations. 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. Nat 5. - PowerPoint PPT PresentationTRANSCRIPT
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Nat 5
Algebraic Algebraic OperationsOperations
Removing Single Brackets - Revision
Removing Double Brackets (ax+b)(cx+d)
Alternative Method FOIL – (NOT TAUGHT)
Solving More equations (x+2)2 =x2 +64
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Removing Harder Double Brackets
Tidying up and Cubing (x+2)3
Exam Questions
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Starter QuestionsStarter Questionsw
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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 =
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Q3. Spilt £64 pounds into the ratio 7:9
Q4. Explain why 0.0675 is equal to 6.75x10-2
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1. We are learning how to multiply out (remove) various single brackets.
1.1. Understand the keypoints Understand the keypoints of multiplying out an of multiplying out an expression with a single expression with a single bracket.bracket.
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Removing aRemoving aSingle BracketSingle Bracket
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3(b + 5) =3b + 15
Example 1
4(w - 2) =4w - 8
Example 2
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Removing aRemoving aSingle BracketSingle Bracket
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Example 3 : Write down an expressionfor the amount indicate belowin two difference ways.
3(x + 3) =3x + 9
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Removing aRemoving aSingle BracketSingle Bracket
x+3
x+3
x+3
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Example 8 : Write down an expressionfor the amount indicate belowin two difference ways.
5(y - 2) = 5y - 10
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Removing aRemoving aSingle BracketSingle Bracket
y-2
y-2 y-2
y-2y-2
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a(b + 5) =ab + 5a
Example 4
p(w - 2) =pw - 2p
Example 5
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Removing aRemoving aSingle BracketSingle Bracket
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y(y - 1) = y2 - y
Example 6
7w(w - 3) =7w2 - 21w
Example 7
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Removing aRemoving aSingle BracketSingle Bracket
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-(x + y) = -x - y
Example 8
-5(a - 7) =-5a + 35
Example 9
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Removing aRemoving aSingle BracketSingle Bracket
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7 + 3(4 - y) =7 + 12
Example 10
9 - 3(8 - y) =9 - 24
Example 11
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Removing aRemoving aSingle BracketSingle Bracket
- 3y= 19 - 3y
Tidy Up
+ 3y
Tidy Up
= -15 + 3y
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4(m - 3) - (m + 2) =4m - 12 - m - 2
Example 12
Example 13
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= 3m - 14
Tidy Up
7(y - 1) - 2(y + 4) =7y - 7 - 2y - 8 = 5y - 15
Tidy Up
Removing Two Single Removing Two Single BracketsBrackets
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Now try Ex 1.1
Ch1 N5 TJ (page 13)
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Removing aRemoving aSingle BracketSingle Bracket
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Starter QuestionsStarter Questionsw
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Q1. Find the area of the shape given
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(w – 5)
3
Q2. Is the following true
-2a( b – a) = -2ab +4a
Q3. Write down the two numbers that multiplyto give 8 and subtract to give 2.
Apr 20, 2023Apr 20, 2023ww
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1. We are learning how to multiply out a pair of brackets using the multiplication table method.
1.1. Understand the keypoints Understand the keypoints of multiplying out paired of multiplying out paired brackets.brackets.
Int 2
2.2. Be able to multiply out Be able to multiply out paired brackets using the paired brackets using the multiplication table multiplication table method.method.
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Removing Removing Double BracketsDouble Brackets
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Below is a floor plan of the down stairs of a house.
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RemovingRemovingDouble BracketsDouble Brackets
y 5
y
3y2+ 8y + 15
Living Room
KitchenBathroom
Bedroom
What is the total area of the
downstairs house?
y2 5y
3y 15
Tidy up !
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Multiplication table for brackets
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RemovingRemovingDouble BracketsDouble Brackets
(y + 3)(y + 5) y+ 3 y+ 5
Double brackets are used in AREA calculations
+5y
+15+3y
y2
y2+ 8y + 15
Example 1
Tidy up !
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Example 2
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RemovingRemovingDouble BracketsDouble Brackets
(2x - 1)(x + 3) 2x - 1 x+ 3
Be careful with the negative
signs
+6x
-3-x
2x2
2x2+ 5x - 3
Tidy up !
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= (x + 1)(x + 1) Example 3 : (x + 1)2
Multiply out the brackets and Simplify
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Squaring Squaring BracketsBrackets
(x + 1)(x + 1) x+ 1 x+ 1
+ x
+ 1+ x
x2
x2+ 2x + 1
Tidy up !
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Example 4 : Find the area of the square.
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Harder BracketsHarder Brackets
(2x - 3y)(2x - 3y) 2x - 3y 2x - 3y
-6xy
+9y2-6xy
4x2
4x2 - 12xy + 9y2
(2x-3y)
Tidy up !
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Example 5
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HarderHarderDouble BracketsDouble Brackets
(x + 4)(x2 + 3x + 2) x+ 4 x2 + 3x
Just a biggerMultiplicatio
n Table
+3x2
+12x+4x2
x3
x3
+ 2
+2x
+8 + 7x2+ 14x+ 8
Tidy up !
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2x
Example 6
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RemovingRemovingDouble BracketsDouble Brackets
(2x - 1)(x2 + 2x - 1) - 1 x2 + 2x
Just a biggerMultiplicatio
n Table
+4x2
-2x-x2
2x3
2x3
- 1
-2x
+1 + 3x2 - 4x+ 1
Tidy up !
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Example 7 :
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Harder BracketsHarder Brackets
-1
- 1
4a2
2a(
(212a
-
2a 2a12a
-2a1
-2a((12a
- 2a((1
2a-
1
4a24a2 - 2
14a2+
Tidy up !
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Now try Ex 1.2
Ch1 N5 TJ (page 14)
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Removing aRemoving aSingle BracketSingle Bracket
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Starter QuestionsStarter Questionsw
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statement True or False?
Q2. Does (w + 2)(w + 1) = w2 + 3w + 2
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Q3.1 254 7
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1. We are learning how to multiply out a pair of brackets using FOIL.
1.1. Understand the keypoints Understand the keypoints of multiplying out double of multiplying out double brackets using FOIL.brackets using FOIL.
Int 2
2.2. Be able to multiply out Be able to multiply out double brackets using double brackets using FOIL.FOIL.
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Removing Removing Double BracketsDouble Brackets
20 Apr 202320 Apr 2023 Created by Mr. Created by Mr. [email protected]@mathsrevision.com
Now try Ex 1.3
Ch1 N5 TJ (page 17)
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Removing aRemoving aSingle BracketSingle Bracket
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We can use the F O I L method to multiply out DOUBLE brackets.
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RemovingRemovingDouble BracketsDouble Brackets
Simply remember the word
F O I LMultiply First 2
Multiply Last 2
Multiply Outside 2
Multiply Inside 2
FOIL Method
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(x + 1)(x + 2)
x2 + 2x
Example 1 : Multiply out the brackets and Simplify
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1. Write down F O I L+ x + 2
2. Tidy up ! x2 + 3x + 2
RemovingRemovingDouble BracketsDouble Brackets
Try again using multiplication
table
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(x - 1)(x + 2)
x2 + 2x
Example 2 : Multiply out the brackets and Simplify
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Removing Removing Double BracketsDouble Brackets
1. Write down F O I L- x - 2
2. Tidy up ! x2 + x - 2
Try again using multiplication
table
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FOIL method is very limited
therefore from now on we will use
the multiplication table method.
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Squaring Squaring BracketsBrackets
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(x + 1)(x - 2)
RemovingRemovingDouble BracketsDouble Brackets
(x - 1)(x - 2)
(x + 3)(x + 2)
(x - 3)(x + 2)
(x + 3)(x - 2)
x2 - x - 2
x2 - 3x + 2
x2 + 5x + 6
x2 - x - 6
x2 + x - 6
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Now try Ex 1.2
Ch1 N5 TJ (page 14)
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Removing aRemoving aSingle BracketSingle Bracket
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Starter QuestionsStarter Questionsw
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Q2. 3 + (-4) x 5
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Q3. Is it true1 1 1
4 4 2
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1. We are learning how to expand and tidy up complicated expressions that include squared and cubed brackets.
1.1. Use techniques learned so Use techniques learned so far to simplify complicated far to simplify complicated brackets.brackets.
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Simplifying Simplifying ExpressionsExpressions
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6m2 - 7m - 3
Example 1
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( m2 – 2m + 1 )
Simplifying Simplifying ExpressionsExpressionsUse multiplication
table to remove brackets.
Tidy up
-
6m2 - 7m - 3- m2 + 2m – 1
5m2 – 5m - 4
YOU need to be VERY CAREFUL !!
(2m - 3)(3m + 1) – (m - 1)2
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(5y – 2)3
(25y2 – 20y + 4)
Example 1
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( 5y – 2)
Simplifying Simplifying ExpressionsExpressionsUse multiplication
table for first two brackets.
125y3 – 150y2 + 60y - 8
(5y – 2)(5y – 2)(5y – 2)
Use multiplication
table again
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Now try Ex 1.3
Ch1 N5 TJ (page 17)
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Simplifying Simplifying ExpressionsExpressions
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Starter QuestionsStarter Questionsw
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Q2. The sun is 92 million mile away from the earth. Write this in standard form.
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Q3. Is it true1 1 5
2 3 6
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1. We are learning how to solve equations that have paired or squared brackets.
1.1. Be able to solve equations Be able to solve equations that contain paired or that contain paired or squared brackets using squared brackets using multiplication table and multiplication table and balancing method.balancing method.
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Equations and Equations and bracketsbrackets
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m(m + 4) =(m + 1)(m+2)
m2 + 4m
Example 1
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= m2 + 3m + 2
Equations and Equations and bracketsbrackets
4m
m = 2
= 3m + 2
12
12
Multiplication table
Balancing Method
Check !
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(x + 5)2 =(x - 5)2
(x + 5)(x + 5)
Example 2
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= (x - 5)(x - 5)
Equations and Equations and bracketsbrackets
x2 + 10x + 25
20x = 0
x = 0
Multiplication table
= x2 – 10x + 2510x + 25= -10x + 25
Balancing Method
25 25
Check !
20 20
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Balancing Method
A = (x + 7)(x – 2)
Example 3 : The two areas are equal. Find the value of x.
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(x + 7)
(x – 2)(x + 2)A = (x + 2)2
(x + 2) (x + 2)2 = (x + 7)(x - 2)
x2 + 4x + 4
x = 18
Multiplication table
Equations and Equations and bracketsbrackets
= x2 + 5x - 14
4x + 4= 5x - 14 5x - 14= 4x + 4
400 400
Check !
Swap !
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Now try Ex 1.4
Ch1 N5 TJ (page 18)
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Equations and Equations and BracketsBrackets