COMBINING LIKE TERMS

Chapter 8.5

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

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

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

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

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

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

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__

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

COMBINING LIKE TERMS

1.2x2 + 3x2

2.5x3 + 2x2

3.7x2y3 – 3x2y3

4.(7x2 + 2x – 3) + (4x2 – x + 5)

Your Turn

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

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.

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

3x2 + 2x – 6– 3x – x2 – 3

Combine like terms I always put the sign in with my

squares or circles

2x2– x – 9

3x2 + 2x – 6– 3x – x2 – 3

Or you can add them Make sure to line them up

properly!

2x2 – x – 9– 3– 3x-x2___________

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

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!

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

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)

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