Solve the Expression: (xy+2a)(x-2b) Binomial Multiplication

To solve the problem $(xy + 2a) \cdot (x - 2b)$, we will use the distributive property, commonly referred to as the FOIL method for binomials. This involves multiplying each term in the first binomial by each term in the second binomial:

• First: Multiply the first terms of each binomial: $xy \times x = x^2y$.
• Outside: Multiply the outer terms: $xy \times (-2b) = -2xyb$.
• Inside: Multiply the inner terms: $2a \times x = 2ax$.
• Last: Multiply the last terms: $2a \times (-2b) = -4ab$.

Next, we combine these four results to form the expanded expression:

$x^2y - 2xyb + 2ax - 4ab$

Thus, the correct expression after using the distributive property and simplifying is $x^2y - 2xyb + 2ax - 4ab$.