Question

use the distributive property to write an equivalent expression without parentheses.
9(a + 8)
check all that apply.

• distribute 9, by multiplication, to the variable, a, and to the constant, 8.
• write the two multiplications, 9(a) + 9(8)
• the expression 9(a) is written as 9a.
• the expression 9(8) equals 72.
• the equivalent expression is 9a + 8.
• the equivalent expression is 9a + 72.

Explanation:

Step1: Recall Distributive Property

The distributive property states that \( c(a + b)=ca+cb \). For \( 9(a + 8) \), we apply this property.

Step2: Distribute 9 to Each Term

Distribute 9 to \( a \) and 8: \( 9(a)+9(8) \).

Step3: Simplify Each Product

\( 9(a) = 9a \) and \( 9(8)=72 \). So the expression becomes \( 9a + 72 \).

Now check the options:

• "Distribute 9, by multiplication, to the variable, \( a \), and to the constant, 8." - Correct, this is the distributive step.
• "Write the two multiplications, \( 9(a)+9(8) \)" - Correct, this is the application of distributive property.
• "The expression \( 9(a) \) is written as \( 9a \)." - Correct, \( 9\times a = 9a \).
• "The expression \( 9(8) \) equals 72." - Correct, \( 9\times8 = 72 \).
• "The equivalent expression is \( 9a + 8 \)." - Incorrect, we have \( 9\times8 = 72 \), not 8.
• "The equivalent expression is \( 9a + 72 \)." - Correct, from the distribution.

Answer:

• Distribute 9, by multiplication, to the variable, \( a \), and to the constant, 8.
• Write the two multiplications, \( 9(a)+9(8) \)
• The expression \( 9(a) \) is written as \( 9a \).
• The expression \( 9(8) \) equals 72.
• The equivalent expression is \( 9a + 72 \).