welcome to the mm204 unit 4 seminar. section 2.7: combining like terms like terms : exactly the...
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Welcome to the MM204
Unit 4 Seminar
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Section 2.7: Combining Like Terms
Like Terms: Exactly the same letter and the same exponent. We need like terms to add and subtract.
Example: 3x and 5x are like terms.
2x3 and 4x are not like terms.
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Like Terms Examples
3x + 8x = 11x
8x + 7y + 2x - 4y = 8x + 2x + 7y – 4y Rearrange if it helps.= 10x + 3y
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Like Terms Example
3x + 5 - 2x2 + 1 - 15x + 9x2
= - 2x2 + 9x2 + 3x - 15x + 5 + 1
I like to rearrange the terms so the like terms are together. This is optional for you.
= 7x2 – 12x + 6
We add (subtract) the numbers in front of the letters and keep the letters the same.
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Like Terms Example
Rearrange the terms (optional).
Get LCDs since we’re adding.
yxyx107
61
43
21
yyxx107
43
61
21
yyxx
22
107
55
43
61
33
21
yyxx2014
2015
61
63
yx2029
64
yx2029
32
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Section 2.8: Evaluating Expressions and Formulas
Evaluating Expressions: We’ll be given an expression and a number to plug in for the
letter(s). Plug in and simplify.
Example: Evaluate 3x - 10y; for x = 1 and y = 4
= 3(1) - 10(4) Substitute the given values into the expression.
= 3 - 40 Multiply.
= -37
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The Importance of Parentheses
2y2 for y = -4= 2(-4)2 We are taking y to the second power.= 2(-4)(-4)= 2(16)= 32
(2y)2 for y = -4= (2(-4))2 We are taking 2y to the second power.= (-8)2
= (-8)(-8)= 64
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Evaluating an Expression Example
Evaluate 2x2 - 5x + 3y2 for x = -2 and y = 4
= 2(-2)2 – 5(-2) + 3(4)2 PEMDAS.
= 2(-2)(-2) - 5(-2) + 3(4)(4)
= 2(4) - 5(-2) + 3(16)
= 8 + 10 + 48
= 18 + 48
= 66
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Formulas Example
#42 on page 101: A field is shaped like a parallelogram. The base measures 92 feet. The altitude measures 54 feet. What is the area of the field?
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Formulas Example
We want to build a fence to enclose a garden. The garden is a rectangle with a width of 10 feet and a length of 23 feet. How much fencing do we need to buy?
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Section 2.9: Grouping Symbols
Grouping Symbols Instead of using parentheses all the time, we can use brackets and
braces, too. We start with the innermost set of symbols and work our way out.
Example: 2 + [3 + 2(x + 5)]
= 2 + [3 + 2x + 10] Use Dist. prop. on innermost set.
= 2 + [13 + 2x] Combine like terms inside brackets.
= 2 + 13 + 2x Take off brackets (addition).
= 15 + 2x … or… 2x + 15 Combine like terms.
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Grouping Symbols Example
Example: 4(x - y) - 2(3x + y)
Use the distributive property to get rid of the parentheses.
= 4x - 4y - 6x - 2y
combine like terms
= -2x - 6y
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Grouping Symbols Example
2a - {6b - 4[a - (b - 3a)]} Start with the innermost set of parentheses.
= 2a - {6b - 4[a - b + 3a]}
= 2a - {6b - 4[4a - b]} Combine like terms inside.
= 2a - {6b - 16a + 4b} Use the dist prop to get rid of the brackets.
= 2a - {10b - 16a} Combine like terms.
= 2a - 10b + 16a Get rid of the braces.
= 18a - 10b
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