Simplifying expressions
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Transcript of Simplifying expressions
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Simplifying Expressions
By Zain Bin Masood
Senior Maths Teacher
At The Intellect School
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Objective
This presentation is designed to give a brief review of simplifying algebraic expressions and evaluating algebraic expressions.
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Algebraic Expressions
An algebraic expression is a collection of real numbers, variables, grouping symbols and operation symbols.
Here are some examples of algebraic expressions.
27,7
5
3
1,4,75 2 xxyxx
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Consider the example:
The terms of the expression are separated by addition. There are 3 terms in this example and they are
.
The coefficient of a variable term is the real number factor. The first term has coefficient of 5. The second term has an unwritten coefficient of 1.
The last term , -7, is called a constant since there is no variable in the term.
75 2 xx
7,,5 2 xx
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Let’s begin with a review of two important skills for simplifying expression, using the Distributive Property and combining like terms. Then we will use both skills in the same simplifying problem.
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Distributive Property
a ( b + c ) = ba + ca
To simplify some expressions we may need to use the Distributive Property
Do you remember it?
Distributive Property
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Examples
Example 1: 6(x + 2)
Distribute the 6.
6 (x + 2) = x(6) + 2(6)
= 6x + 12
Example 2: -4(x – 3)
Distribute the –4.
-4 (x – 3) = x(-4) –3(-4)
= -4x + 12
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Practice Problem
Try the Distributive Property on -7 ( x – 2 ) .
Be sure to multiply each term by a –7.
-7 ( x – 2 ) = x(-7) – 2(-7)
= -7x + 14
Notice when a negative is distributed all the signs of the terms in the ( )’s change.
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Examples with 1 and –1.
Example 3: (x – 2)
= 1( x – 2 )
= x(1) – 2(1)
= x - 2
Notice multiplying by a 1 does nothing to the expression in the ( )’s.
Example 4: -(4x – 3)
= -1(4x – 3)
= 4x(-1) – 3(-1)
= -4x + 3
Notice that multiplying by a –1 changes the signs of each term in the ( )’s.
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Like Terms
Like terms are terms with the same variables raised to the same power.
Hint: The idea is that the variable part of the terms must be identical for them to be like terms.
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Examples
Like Terms
5x , -14x
-6.7xy , 02xy
The variable factors are
identical.
Unlike Terms
5x , 8y
The variable factors are
not identical.
22 8,3 xyyx
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Combining Like Terms
Recall the Distributive Property
a (b + c) = b(a) +c(a)
To see how like terms are combined use the
Distributive Property in reverse.
5x + 7x = x (5 + 7)
= x (12)
= 12x
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Example
All that work is not necessary every time.
Simply identify the like terms and add their
coefficients.
4x + 7y – x + 5y = 4x – x + 7y +5y
= 3x + 12y
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Collecting Like Terms Example
31316
terms.likeCombine
31334124
terms.theReorder
33124134
2
22
22
yxx
yxxxx
xxxyx
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Both Skills
This example requires both the Distributive
Property and combining like terms.
5(x – 2) –3(2x – 7)
Distribute the 5 and the –3.
x(5) - 2(5) + 2x(-3) - 7(-3)
5x – 10 – 6x + 21
Combine like terms.
- x+11
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Simplifying Example
431062
1 xx
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Simplifying Example
Distribute. 43106
2
1 xx
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Simplifying Example
Distribute. 43106
2
1 xx
12353
3432
110
2
16
xx
xx
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Simplifying Example
Distribute.
Combine like terms.
431062
1 xx
12353
3432
110
2
16
xx
xx
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Simplifying Example
Distribute.
Combine like terms.
431062
1 xx
12353
3432
110
2
16
xx
xx
76 x
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Evaluating Expressions
Remember to use correct order of operations.
Evaluate the expression 2x – 3xy +4y when
x = 3 and y = -5.
To find the numerical value of the expression, simply replace the variables in the expression with the appropriate number.
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Example
Evaluate 2x–3xy +4y when x = 3 and y = -5.
Substitute in the numbers.
2(3) – 3(3)(-5) + 4(-5)
Use correct order of operations.
6 + 45 – 20
51 – 20
31
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Evaluating Example
1and2when34Evaluate 22 yxyxyx
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Evaluating Example
Substitute in the numbers.
1and2when34Evaluate 22 yxyxyx
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Evaluating Example
Substitute in the numbers.
1and2when34Evaluate 22 yxyxyx
22 131242
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Evaluating Example
Remember correct order of operations.
1and2when34Evaluate 22 yxyxyx
22 131242
Substitute in the numbers.
131244
384
15
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Common Mistakes
Incorrect Correct
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