chapter 8.5. c ombining l ike t erms lesson objective: ncscos 1.01 – write the equivalent forms...
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COMBINING LIKE TERMS
Chapter 8.5
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COMBINING LIKE TERMS
Lesson Objective: NCSCOS 1.01 – Write the equivalent forms of algebraic expressions to solve problems
Students will know how to add and subtract polynomials using the concept of “like terms.”
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COMBINING LIKE TERMS
*Like Terms – Like terms must all have the same letters and each letter must have the same exponent.
Like terms can be added and subtracted from each other.
This is called “combining like terms”.
If they are not like terms they cannot be added or subtracted from each other.
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COMBINING LIKE TERMS
Example 1: Solve 3x2 + 5x2
3x2 and 5x2 are “like terms” because they both contain an x and both of the x’s are squared
When we combine like terms either add or subtract the numbers, but the variable will not change
Therefore we can combine 3x2 and 5x2 together and get 8x2
= 8x2
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COMBINING LIKE TERMS
Example 2: Solve 4x3 + 4x2
4x3 and 4x2 are not “like terms” because the x’s have different exponents
Therefore they cannot be combined
= 4x3 + 4x2
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COMBINING LIKE TERMS
Example 3: Solve 3x2y3 + 5x2y3
3x2y3 and 5x2y3 are “like terms” because they both have x’s and y’s and the exponents for both x and y are the same.
We can combine them
= 8x2y3
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COMBINING LIKE TERMS
Example 4: Solve 4x2y3 + 4x2y5
4x2y3 and 4x2y5 are not like terms because the exponents on the y’s are different
These cannot be combined
= 4x2y3 + 4x2y5
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COMBINING LIKE TERMS
Example 5: Find (2x2 + x – 8) + (3x – 4x2 + 2)
Combine like terms: (2x2 + x – 8) + (3x – 4x2 + 2)
( ) + ( ) + ( ) Add them and write your answer:
-2x2 + 4x – 6 Rule: When adding polynomials you just
combine the like terms. Remember minus signs are a negative for the number right after it!
2x2 – 4x2
x + 3x
-8 + 2
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COMBINING LIKE TERMS
Example 5: Find (2x2 + x – 8) + (3x – 4x2 + 2)
Let’s try this a different way We can set up this addition problems
like: 2+ 3__
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COMBINING LIKE TERMS
Let’s do the same with our problem
Make sure the numbers line up properly when you do it!
Now add them up
(2x2 + x – 8) – 4x23x + 2+ + 3x– 4x2 + 2___________
-2x2+ 4x- 6
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COMBINING LIKE TERMS
1.2x2 + 3x2
2.5x3 + 2x2
3.7x2y3 – 3x2y3
4.(7x2 + 2x – 3) + (4x2 – x + 5)
Your Turn
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COMBINING LIKE TERMS
1.2x2 + 3x2
2.5x3 + 2x2
3.7x2y3 – 3x2y3
4.(7x2 + 2x – 3) + (4x2 – x + 5)
Your Turn5x2
5x3 + 2x2
4x2y3
11x2 + x + 2
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COMBINING LIKE TERMS
Example 6: Find (3x2 + 2x – 6) – (3x + x2 + 3) Distribute the negative sign into the
parenthesis: (3x2 + 2x – 6) – (3x + x2 + 3) (3x2 + 2x – 6) + (–3x – x2 – 3) Combine like terms:
(3x2 – x2) + (2x – 3x) + (-6 – 3) Add them and write your answer: 2x2 – x – 9 Rule: When subtracting polynomials you
must first distribute the negative into the parenthesis before combining like terms.
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Example 6: Find
(3x2 + 2x – 6)– (3x + x2 + 3)
First, distribute the negative into the parenthesis after it
Now all the parenthesis can go away
3x2 + 2x – 6– 3x – x2 – 3
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3x2 + 2x – 6– 3x – x2 – 3
Combine like terms I always put the sign in with my
squares or circles
2x2– x – 9
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3x2 + 2x – 6– 3x – x2 – 3
Or you can add them Make sure to line them up
properly!
2x2 – x – 9– 3– 3x-x2___________
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COMBINING LIKE TERMS
Example: (2x2 + 3x – 1) + (5x2 – 3x + 5)
Combine like terms *If two numbers add up to zero, do
not write them in the final answer.
(2x2 + 5x2) + (3x – 3x) + (-1 + 5)
7x2 + 4
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COMBINING LIKE TERMS
1. (7x2 + 2x – 3) – (4x2 – x + 5)
2.(5x3 – 2x2 + 4) – (3x3 + 2x – 2)
3.(3x2 + 4x – 2) – (6x2 + 4x – 5)
Last Practice!
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COMBINING LIKE TERMS
1. (7x2 + 2x – 3) – (4x2 – x + 5)
2.(5x3 – 2x2 + 4) – (3x3 + 2x – 2)
3.(3x2 + 4x – 2) – (6x2 + 4x – 5)
Last Practice!
3x2 + 3x – 8
2x3 – 2x2 – 2x + 6
-3x2 + 3
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COMBINING LIKE TERMS
1.3x2 + 5x – 2x2
Quiz 8.5
2. (3x2 + 2x + 4) + (4x2 – x + 6)3. (2x3 – 3x2 + 5) – (x3 – 2x – 2)4. (6x2 + 2x – 2) – (3x2 + 2x – 5)
5. (5x2y3 – 2xy + 4y2) – (2x2y3 + 5x3 – 5xy)
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COMBINING LIKE TERMS
1.3x2 + 5x – 2x2
Quiz 8.5
2. (3x2 + 2x + 4) + (4x2 – x + 6)3. (2x3 – 3x2 + 5) – (x3 – 2x – 2)4. (6x2 + 2x – 2) – (3x2 + 2x – 5)
5. (5x2y3 – 2xy + 4y2) – (2x2y3 + 5x3 – 5xy)
x2 + 5x
7x2 + x + 10
x3 – 3x2 + 2x + 73x2 + 3
-5x3 + 3x2y3 + 3xy + 4y2