Multiply `(a+b)` by `(c+d)`

Answer

To multiply the expressions \((a + b)\) and \((c + d)\), we will use the distributive property, also known as the FOIL method (First, Outside, Inside, Last) for binomials. Here’s a step-by-step solution:

### Step 1: Write down the expression
We start with the expression:
\[ (a + b)(c + d) \]

### Step 2: Distribute \(a\) to both terms in the second bracket
First, we will multiply \(a\) by each term in the second bracket \((c + d)\):
\[ a \cdot c + a \cdot d \]
This gives us:
\[ ac + ad \]

### Step 3: Distribute \(b\) to both terms in the second bracket
Next, we will multiply \(b\) by each term in the second bracket \((c + d)\):
\[ b \cdot c + b \cdot d \]
This gives us:
\[ bc + bd \]

### Step 4: Combine all the terms
Now, we combine all the terms we obtained from the distributions:
\[ ac + ad + bc + bd \]

### Final Result
Thus, the product of \((a + b)\) and \((c + d)\) is:
\[ ac + ad + bc + bd \]

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