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.
$d + d$
$=\square d + 1d$ identity property of multiplication
$=(1 + 1)\square$
$=\square d$ add

Explanation:

Step1: Apply identity property of multiplication

The identity property of multiplication states that \(a\times1 = a\). So, \(d = 1\times d=1d\). Therefore, \(d + d=1d + 1d\). So the first box is \(1\).

Step2: Apply distributive property of multiplication over addition

The distributive property is \(ac+bc=(a + b)c\). Here, \(a = 1\), \(b = 1\) and \(c = d\). So \(1d+1d=(1 + 1)d\). So the second box is \(d\) and the property is the distributive property of multiplication over addition.

Step3: Add the numbers inside the parentheses

\(1+1 = 2\), so \((1 + 1)d=2d\). So the third box is \(2\).

Answer:

First box: \(1\)
Second box: \(d\) (property: distributive property of multiplication over addition)
Third box: \(2\)