pythagorean theorem, progress report on my · pythagorean theorem to find the hyp addl to find the...
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Day 8 Module 2 Review notes.notebook
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September 06, 2018
Warm-Up 9/6/181. Bring out your Module 2
Study Guide2. Turn in all missing HW! -
Pythagorean Theorem, etc........
3. Turn in your signed Progress Report on my table.
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Day 8 Module 2 Review notes.notebook
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Module 2 Study Guide 9/6/18
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Attachments
Exponent Properties Practice 82416.ksipa
CombineLikeTerms.ppt
SMART Notebook
Combine Like Terms
I can simplify expressions with several variables by combining like terms.
Vocabulary
Constant
A number with nothing else attached to it.
Examples: 1, 2, 47, 925
Vocabulary
Variable
A letter that represents an unknown number.
Examples: a, b, x, y
Vocabulary
Coefficient
The number in front of the variable.
Examples: 3x 3 is the coefficient
2x 2 is the coefficient
Like Terms:
In an expression, like terms are the terms that have the same variables, raised to the same powers (same exponents).
Examples: 4x and -3x or 2y2 and –y2
Like terms because each term consists of a single variable, x, and a numeric coefficient:
2x, 45x, x, 0x, -26x, -x
Like terms because they are all constants:
15, -2, 27, 9043, 0.6
Like terms because they are all y² with a coefficient: 3y², y², -y², 26y²
What are unlike terms?
The following two terms both have a single variable, but the terms are not alike since different variables are used: 17x, 17z
Each y variable in the terms below has a different exponent, therefore these are unlike terms: 15y, 19y², 31y5
Although both terms below have an x variable, only one term has the y variable, thus these are not like terms either: 19x, 14xy
Combine Like Terms
I can simplify expressions with several variables by combining like terms.
Like Terms – same variable with same exponent
6x + 2x =
When combining like terms, only use the coefficients.
6x + 2x =
8x
4x + 3y – 2x + 4y =
Simplify
2x + 7y
Simplify
Never, NEVER, combine x’s and y’s or constant terms with variable terms. 2x + 7y ≠ 9xy and 3a + 6 ≠ 9a.
Key Skills
5 cats + 3 cats
8 cats
5a + 3a
8a
5 apples + 3 oranges
5 apples + 3 oranges
5 cats + 3 dogs
5 cats + 3 dogs
You Try
3y + 2 + 3x – y + 5x
x + x
Distribute by multiplication:
15n and 20 are not alike and therefore cannot be combined. The answer 15n + 20 is simplified because we do not know what the value of n is at this time and cannot complete the multiplication part of this problem.
The Distributive Property
Expressions with variables:
Simplify 5(3n + 4).
No symbol between the 5 and the parenthesis indicates a multiplication problem.
The constant terms 8 and 6 can be combined to form the constant number 14. The answer 28n + 14 is simplified because we do not know what the value of n is at this time and cannot complete the multiplication part of this problem.
The Distributive Property
Simplify 4(7n + 2) + 6.
No symbol between the 4 and the parenthesis indicates a multiplication problem.
Step 1) Use the Distributive Property 3 (2x – 5) - 2x
Step 2) Combine Like Terms6x – 15 – 2x
*** 6x and 2x are like terms!!!!
Step 3) Simplified Expression4x – 15
Distributive Property
Distributive Property
Example:
6(a + 3)Use the Distributive Property
(6a) + (6 x 3)Multiply
6a + 18Simplified
***CAN NOT add 6a + 18 together because they are not like terms.
Solve: 2x + 6(x + 1)
Explain how each of the below answers are wrong and why.
2x + 6x + 1
9x
Practice Problems
=
+
)
4
3
(
5
n
)
3
(
5
n
+
)
4
(
5
=
n
15
20
=
+
+
6
)
2
7
(
4
n
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7
(
4
n
)
2
(
4
n
28
8
6
14
SMART Notebook
Page 1: Sep 4-10:33 PMPage 2: Sep 6-2:53 AMPage 3: Sep 4-10:34 PMPage 4: Sep 4-10:35 PMPage 5: Sep 4-10:36 PMPage 6: Sep 4-10:36 PMPage 7: Sep 4-10:36 PMPage 8: Sep 4-10:37 PMPage 9: Sep 4-10:37 PMPage 10: Sep 4-10:38 PMPage 11: Sep 4-10:39 PMPage 12: Sep 4-10:39 PMPage 13: Sep 4-10:39 PMAttachments Page 1