Complete the Expression: (76+2a)(□+□)=152x+76b+4ax+2ab

Fill in the missing value:

$(76+2a)(?+?)=152x+76b+4ax+2ab$

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

• Step 1: Assume the missing values in the expression are $b$ and $2x$.

• Step 2: Expand the binomial expression $(76+2a)(b+2x)$ using the distributive property.

• Step 3: Match the expanded result with the right-hand expression $152x+76b+4ax+2ab$.

Now, let's work through each step:

Step 1: The binomial expression is $(76 + 2a)(b + 2x)$.

Step 2: Expanding this expression using the distributive property, we have:

$\begin{aligned} (76 + 2a)(b + 2x) &= 76b + 76(2x) + 2a(b) + 2a(2x) \\ &= 76b + 152x + 2ab + 4ax. \end{aligned}$

Step 3: Comparing this with the expression on the right side, $152x+76b+4ax+2ab$, we find they match perfectly.

Therefore, the missing values are $b$ and $2x$, which corresponds to choice $2$.