1. The problem is to multiply two binomials using the extended method (also known as the FOIL method). Let's consider the binomials $(a+b)$ and $(c+d)$. 2. The extended method multiplies each term in the first binomial by each term in the second binomial: $$ (a+b)(c+d) = a \cdot c + a \cdot d + b \cdot c + b \cdot d $$ 3. Simplify the expression by carrying out the multiplications: $$ = ac + ad + bc + bd $$ 4. This is the expanded form of the product of two binomials. If you have a specific example or values for $a$, $b$, $c$, and $d$, please provide them for a detailed solution.