Ac + ad + 3bd + 3bc

The expression you've provided is \( ac + ad + 3bd + 3bc \). To simplify or factor this expression, we can look for common factors in pairs of terms. 1. **Grouping Terms:** We can group the terms as follows: \[ (ac + ad) + (3bd + 3bc) \] 2. **Factoring Out Common Factors:** - From the first group \( ac + ad \), we can factor out \( a \): \[ a(c + d) \] - From the second group \( 3bd + 3bc \), we can factor out \( 3b \): \[ 3b(d + c) \quad \text{(noting that } d + c = c + d\text{)} \] 3. **Combining the Factored Terms:** Now, we can write the expression as: \[ a(c + d) + 3b(c + d) \] Since \( (c + d) \) is common in both terms, we can factor that out as well: \[ (c + d)(a + 3b) \] Thus, the simplified and factored form of the expression \( ac + ad + 3bd + 3bc \) is: \[ (c + d)(a + 3b) \]