Question

complete the expressions and select the missing properties.
write each answer as a number, a variable, or the product of a number and a variable.
9(2 + 2q)
= 9·2 + 9·□
= □ + 18q \tmultiply
= 18q + □

Explanation:

Step1: Apply Distributive Property

The distributive property states that \( a(b + c)=a\cdot b + a\cdot c \). For \( 9(2 + 2q) \), we distribute 9 to both terms inside the parentheses. So \( 9(2 + 2q)=9\cdot2 + 9\cdot2q \). So the first missing box is \( 2q \).

Step2: Multiply 9 and 2

Calculate \( 9\cdot2 \). \( 9\times2 = 18 \). So the second missing box is 18.

Step3: Apply Commutative Property of Addition

The commutative property of addition states that \( a + b=b + a \). So \( 18 + 18q=18q + 18 \). So the third missing box is 18. The property for the last step is the commutative property of addition.

Answer:

First box: \( 2q \)
Second box: \( 18 \)
Third box: \( 18 \)
First property: Distributive Property (for the first step)
Last property: Commutative Property of Addition (for the last step)

(For the dropdowns: First dropdown - Distributive Property; Last dropdown - Commutative Property of Addition)