Download Combining Like Terms

Chapter 8.5
COMBINING LIKE TERMS
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.”
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.
COMBINING LIKE TERMS
 Example 1: Solve 3x2 + 5x2 = 8x2
 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
COMBINING LIKE TERMS
 Example 2: Solve 4x3 + 4x2 = 4x3 + 4x2
 4x3 and 4x2 are not “like terms” because
the x’s have different exponents
 Therefore they cannot be combined
COMBINING LIKE TERMS
 Example 3: Solve 3x2y3 + 5x2y3 = 8x2y3
 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
COMBINING LIKE TERMS
 Example 4: Solve 4x2y3 + 4x2y5
= 4x2y3 + 4x2y5
 4x2y3 and 4x2y5 are not like terms because
the exponents on the y’s are different
 These cannot be combined
COMBINING LIKE TERMS
 Example 5: Find (2x2 + x – 8) + (3x – 4x2 + 2)
 Combine like terms:
(2x2 + x – 8) + (3x – 4x2 + 2)
 (2x2 – 4x2 ) + (x + 3x ) + (-8 + 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!
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:
COMBINING LIKE TERMS
2
(2x
+ x – 8)
 Let’s do the same with
our problem
 Make sure the
numbers line up
properly when you do
it!
 Now add them up
COMBINING LIKE TERMS
1. 2x2 + 3x2
2. 5x3 + 2x2
3. 7x2y3 – 3x2y3
4. (7x2 + 2x – 3) + (4x2 – x + 5)
COMBINING LIKE TERMS
1. 2x2 + 3x2 5x2
3 + 2x2
3
2
5x
2. 5x + 2x
3. 7x2y3 – 3x2y3 4x2y3
4. (7x2 + 2x – 3) + (4x2 – x + 5)
3x2 + x + 2
 Example 6: Find
 First, distribute the negative into the
parenthesis after it
 Now all the parenthesis can go away
 Combine like terms
 I always put the sign in with my squares or
circles
 Or you can add them
 Make sure to line them up properly!
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.
COMBINING LIKE TERMS
1. (7x2 + 2x – 3) – (4x2 – x + 5)
2. (5x3 – 2x2 + 4) – (3x3 + 2x – 2)
3. (3x2 + 4x – 2) – (6x2 + 4x – 5)
COMBINING LIKE TERMS
1. (7x2 + 2x – 3) – (4x2 – x + 5)
2
3x
+ 3x – 8
2. (5x3 – 2x2 + 4) – (3x3 + 2x – 2)
3
2
2x – 2x – 2x + 6
3. (3x2 + 4x – 2) – (6x2 + 4x – 5)
-3x2 + 3
COMBINING LIKE TERMS
1. 3x2 + 5x – 2x2
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)
COMBINING LIKE TERMS
1. 3x2 + 5x – 2x2
x2 + 5x
2. (3x2 + 2x + 4) + (4x2 – x + 6)
7x2 + x + 10
3. (2x3 – 3x2 + 5) – (x3 – 2x – 2)
x3 – 3x2 + 2x + 7
2 + 2x – 5)
4. (6x2 + 2x
–
2)
–
(3x
3x2 + 3
5. (5x2y3 – 2xy + 4y2) – (2x2y3 + 5x3 – 5xy)
-5x3 + 3x2y3 + 3xy + 4y2