Question

writing about creating equivalent expressions
explain how to write an equivalent expression using the distributive property.
2(11 + y)
22+2y
sample response: to use the distributive property, distribute multiplication by 2 to both terms inside the parentheses. the products are 2(11) and 2(y). the equivalent expression is 22 + 2y.
check all points that you included in your response.
□ to use the distributive property, distribute multiplication by 2 to both terms inside the parentheses.
□ the products are 2(11) and 2(y).
□ the equivalent expression is 22 + 2y.

Explanation:

Step1: Recall Distributive Property

The distributive property is \( a(b + c)=ab + ac \). For \( 2(11 + y) \), \( a = 2 \), \( b = 11 \), \( c = y \).

Step2: Apply Distributive Property

Multiply 2 with 11 and 2 with y: \( 2\times11+2\times y \).

Step3: Simplify the Products

\( 2\times11 = 22 \) and \( 2\times y=2y \), so the expression becomes \( 22 + 2y \).

Answer:

To write an equivalent expression for \( 2(11 + y) \) using the distributive property:

1. Recall the distributive property: \( a(b + c)=ab + ac \). Here, \( a = 2 \), \( b = 11 \), \( c = y \).
2. Distribute 2 to both terms inside the parentheses: \( 2\times11+2\times y \).
3. Simplify the products: \( 2\times11 = 22 \) and \( 2\times y = 2y \), so the equivalent expression is \( 22 + 2y \).

For the check - all - that - apply questions:

• "To use the distributive property, distribute multiplication by 2 to both terms inside the parentheses." is correct.
• "The products are \( 2(11) \) and \( 2(y) \)." is correct (since \( 2(11)=2\times11 \) and \( 2(y)=2\times y \)).
• "The equivalent expression is \( 22 + 2y \)." is correct (as shown by applying the distributive property).