1. **State the problem:** Factorize the expression $$(x+4)(3x+11)-(x+4)(6x+7)$$. 2. **Identify common factors:** Notice that both terms have a common factor of $$(x+4)$$. 3. **Use the distributive property:** Factor out $$(x+4)$$: $$ (x+4)(3x+11) - (x+4)(6x+7) = (x+4)\big[(3x+11) - (6x+7)\] $$ 4. **Simplify inside the brackets:** $$ (3x+11) - (6x+7) = 3x + 11 - 6x - 7 = (3x - 6x) + (11 - 7) = -3x + 4 $$ 5. **Write the final factorized form:** $$ (x+4)(-3x + 4) $$ 6. **Optional:** You can write it as $$ (x+4)(4 - 3x) $$ This is the fully factorized form of the original expression.