Solve (a+8)(b+7) - Missing Term = 7a+8b: Algebraic Expansion Challenge

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

• Step 1: Expand the expression $(a+8)(b+7)$ using the distributive property.
• Step 2: Compare the expanded terms with $7a + 8b$ to find the missing part.
• Step 3: Identify the correct expression to fill the blank.

Now, let's work through each step:
Step 1: Expand the expression $(a+8)(b+7)$.
Using the distributive property: $(a+8)(b+7) = a(b+7) + 8(b+7)$ $= ab + 7a + 8b + 56$ Step 2: Compare the expanded terms with the given equation. We have: $ab + 7a + 8b + 56 - ▭ = 7a + 8b$ Subtract $7a + 8b$ from both sides: $ab + 7a + 8b + 56 - ▭ - 7a - 8b = 0$ This simplifies to: $ab + 56 - ▭ = 0$ Step 3: Solving for the missing part, we find: $▭ = ab + 56$ Therefore, the expression that fills in the blank is $ab+56$.

The correct choice from the options provided is:

$ab+56$