Transcript Number

Algebra
Saturday, 16 September 2006
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Notes
Expressions and Equations
An equation has an equal sign.
An expression doesn’t.
Which are expressions and
which are equations ?
2x + 1 = 8
Expression
Expression
Saturday, 16 September 2006
3x – 8
4–x
7x – 6 = 7
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Equation
Equation
Notes
Using Letters for numbers
Write an expression for this statement:
I start with x, double it and then add 8
x
double
2x
add 8
The expression is: 2x + 8
Saturday, 16 September 2006
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2x + 8
Exercise
1. Write expressions for the following:
a) Start with x, double it and then subtract 7
a) 2x – 7
b) Start with x, add 5 then double the result
b) 2(x + 5)
c)
c)
Start with x, multiply by 7 then take away 5
7x – 5
d) Start with x, add y then double the result
d) 2(x + y)
e) Start with x, add 6 then square the result
e) (x + 6)
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2
Notes
Collecting like terms
• In the expression 2x + 1, both 2x and 1 are called terms.
• Terms can be collected if they are the same type.
Examples
1. 2x + 3x + 1 = 5x + 1
2. 4x + 3 + 2x –1 = 6x + 2
3. 6x + 7y – 2x – 4y = 4x + 3y
4. x² + 3x² + x + 4x = 4x² + 5x
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x and y are unlike terms
x² and y² are unlike terms
Exercise
1. Collect like terms
a)
b)
c)
d)
e)
2x + 3 + 3x + 5
5x – 3 + 4x + 8
9x – 9 + 2x – 3 – 6x
12a + 4b + 7b – 5a
x² + 5x + 4 – 3x + 7 + 3x²
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a)
b)
c)
d)
e)
5x + 8
9x + 5
5x – 12
7a + 11b
4x² + 2x + 11
Notes
Expanding Brackets (Multiplying out brackets)
• Here are some examples of expanding brackets.
• Everything inside the bracket is multiplied by the term
outside.
Examples
1.
2.
3.
4.
5.
2(x + 1) = 2x + 1
3(2x – 3) = 6x – 9
-4(x + 4) = -4x –16
-2(2x – 3) = -4x + 6
x(x + 2) = x² + 2x
Saturday, 16 September 2006
Careful
with signs
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Exercise
1. Expand these brackets
a)
b)
c)
d)
e)
f)
g)
h)
i)
j)
2(x + 10)
3(2x – 9)
4(2x – 3)
5(3 + 3x)
-10(2x + 3)
-3(5 – 2x)
x(x + 9)
2x(x – 3)
3x(4x + 2)
2x²(x – 1)
Saturday, 16 September 2006
a)
b)
c)
d)
e)
f)
g)
h)
i)
j)
2x + 20
6x – 27
8x – 12
15 + 15x
-20x – 30
-15 + 6x
x² + 9x
2x² - 6x
12x² + 6x
2x3 – 2x²
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Notes
Expanding Brackets and simplifying
• Easy – expand the brackets first and then collect like terms
Examples
1. 2(x + 1) + 3(x + 2)
2. 3(x – 2) – 2(x + 1)
= 2x + 2 + 3x + 6
= 5x + 8
= 3x – 6 –2x –2
=x-8
Careful
with signs
Saturday, 16 September 2006
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Exercise
1. Expand and simplify
a) 2(x + 2) + 4(x + 1)
a) 2x + 4 + 4x + 4 = 6x + 8
b) 2(x – 3) + 3(x + 3)
b) 2x – 6 + 3x + 9 = 5x + 3
c)
c)
7(x – 2) + (x + 4)
7x – 14 + x + 4 = 8x – 10
d) 6(x – 2) – (2x + 9)
d) 6x – 12 – 2x – 18 = 4x – 30
e) 2(2 + x) + 3(x – 1)
e) 4 + 2x + 3x – 3 = 5x + 1
Saturday, 16 September 2006
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