Moving Straight Ahead

Lesson 3: More with Combining Like Terms

EQ: How can I combine like terms that have multiple variables and/or

exponents?

• Sometimes an expression includes terms that have multiple variables and/or exponents

• Steps to simplify:• 1. Identify like terms (the variables and

exponents behind the coefficients must match exactly)

• 2. Combine like terms (by adding the coefficients)

3xy2 – 4x + 12x2 + 4xy2 -2x

1st Step: Identify the Like Terms

2nd Step: Combine Like Terms

Example

1:

-7a2b – 2ab2 + 8a – 6ab2 – 3a

1st Step: Identify the Like Terms

2nd Step: Combine Like Terms

Example

2:

Try These:

1. -10t2 + 4s3t – 9t3 -2t2 + 12t3 - 4s3t

1. p2 + 2r3 – 17p2 –r3 + rs -10rs + r3

1. 14xy4 + 17xy – 14xy + 3xy3 – 2xy4 -12xy3 + 5xy2

EQ: How can I use the distributive property to

simplify algebraic expressions?

Review:

What is the distributive property?

Simplify the expression using the distributive property.

4(3x + 5) =

-2 (4 – x) =

What do you do if…There is a negative number being distributed?

Let’s find out! Here’s an example…

- ( 4x – 5y) (- 1)(4x) – (-1)(5y)

ANSWER: -4x +5y

Adding and Subtracting Linear Expressions

Step 1: Distribute any negatives and/or terms outside the parentheses

Step 2: Identify Like Terms

Step 3: Combine Like Terms

EXAMPLE:

(3b + 4a) – (2b – 8a)

Answer: 12a + b

Don’t forgetto distribute the negative

before combining like

terms

Let’s practice…

1. (-4c + 2d) + ( 2c – 5d)

1. (8m + 12 v) - (10 m – 5v)

Don’t forgetto distribute the negative

before combining like

terms

3. -(7x – 4 y) – (x – 12y)

4. -2(9z + 6g) – (-7g + z) + 8g

Don’t forgetto distribute the negative

before combining like

terms