Question

complete the expressions and select the missing property.
write each answer as a number, a variable, or the product of a number and a variable.
$4y + 4y$
$=(4 + 4)\square$
$=\square y$
add

Explanation:

Step1: Apply Distributive Property

The distributive property states that \(a \cdot c + b \cdot c=(a + b)\cdot c\). For \(4y+4y\), we can factor out the common variable \(y\), so \(4y + 4y=(4 + 4)y\). So the first box should be filled with \(y\), and the property used here is the distributive property (or reverse of distributive property, also known as factoring).

Step2: Add the Coefficients

Now we calculate \(4 + 4\). \(4+4 = 8\), so \((4 + 4)y=8y\).

Answer:

First box: \(y\), Property: Distributive Property (or Distributive Property of Multiplication over Addition, or Factoring), Second box: \(8\)