Simplify 2a(b+3)+4(b+3): Finding Equivalent Expressions

Which of the expressions is equivalent to the expression?

$2a(b+3)+4(b+3)$

To solve this problem, we'll follow these steps:

• Step 1: Identify the common factor in the expression.
• Step 2: Factor out the common factor using the distributive property.
• Step 3: Simplify the expression inside the parentheses.

Now, let's work through each step:

Step 1: Identify the common factor. The given expression is $2a(b+3) + 4(b+3)$. Notice that both terms have a common factor, which is $(b+3)$.

Step 2: Factor out the common factor. Using the distributive property in reverse, we can factor out $(b+3)$:

Step 3: Simplify the expression inside the parentheses if needed. In this case, $2a + 4$ is already simplified.

Therefore, the expression $2a(b+3) + 4(b+3)$ simplifies to the equivalent expression $(b+3)(2a+4)$.

The correct choice that corresponds to this expression is choice 3: $(b+3)(2a+4)$.