Question

Which expression is equivalent to 4(12 + 5) + 3?

Option 1: 48 + 5 + 3
Option 2: 4(12) + 4(5) + 3
Option 3: 48 + 4 + 3
Option 4: 4 + 17 + 3

Answer 1

The equivalent expression to 4(12 + 5) + 3 is Option 2: 4(12) + 4(5) + 3, as it applies the distributive property to distribute the 4 and then combine like terms.

Step-by-step explanation:

The student is asking which expression is equivalent to 4(12 + 5) + 3. To find an equivalent expression, we can use the distributive property, which states that a(b + c) = ab + ac. Applying this property to the given expression:

4(12) + 4(5) + 3

This simplifies to:

48 + 20 + 3

By combining like terms, we get:

68 + 3 = 71

So the expression equivalent to 4(12 + 5) + 3 is Option 2: 4(12) + 4(5) + 3, as it correctly applies the distributive property before combining like terms to reach the final result.