### Student Page1.6.5Combining Like Terms A4US

#### 1.

Find the area of each of the algebra tiles shown. The side lengths are labeled. The variable, $$x\text{,}$$ represents an unknown length. #### 2.

Translate each of the figures into algebra. Explain your translation. Simplify each expression as much as possible and explain why you cannot simplify further.

##### (a) ##### (b) ##### (c) ##### (d) #### 3.

Draw algebra tiles to illustrate each expression. Use your illustration to simplify each of the algebraic expressions. Explain how you know you are correct.

##### (a)

$$2x + 4 + 3x + 7 =$$

##### (b)

$$4x + 8 - 3x + 2 =$$

##### (c)

$$3x + 8 - (4x + 2) =$$

##### (d)

$$7x - 2(3x - 1) + x =$$

#### 4.

Summarize your work with combining like terms. Which terms can you combine? How do you know?

#### 5.

Simplify the following expressions. Show and explain your work.

##### (a)

$$3 + 5x - x + 7 =$$

##### (b)

$$3 + 5x - (x + 7) =$$

##### (c)

$$4 + 2(x - 1) =$$

##### (d)

$$15x - 4(2 - 3x) + 7 =$$