which expression uses the communtative property of addition and the associate property of multiplication to rewrite the expression 3x(2x8)+7

Answer 1

To rewrite the expression \(3x(2 \times 8) + 7\) using the commutative property of addition and the associative property of multiplication, we can first recognize what those properties entail:

• Commutative Property of Addition states that \(a + b = b + a\).
• Associative Property of Multiplication states that \(a(bc) = (ab)c\).

Let's first calculate \(2 \times 8\):

\[ 2 \times 8 = 16 \]

Substituting that back into the expression gives us:

\[ 3x(16) + 7 \]

Now we apply the properties:

1. Using the associative property within the multiplication: We can express \(3x(16)\) in a different way: \[ = (3x \times 16) \]

2. Now, let’s apply the commutative property so that we can rearrange the addition: \[ 3x(16) + 7 = 7 + 3x(16) \]

So, rewriting the expression while utilizing both properties, we have:

\[ 7 + 3x(16) \]

In its final form, the expression is \(7 + 3x(16)\), which incorporates both the commutative property of addition and the associative property of multiplication.