39) \( 56 a b+14-49 a-16 b \)

To simplify the expression \( 56ab + 14 - 49a - 16b \), we can rearrange it as \( -49a + 56ab - 16b + 14 \). Now we can factor by grouping or look for common terms. Notice that we cannot factor it neatly, but we can express it in a more organized form, resulting in a simplified expression: \( 56ab - 49a - 16b + 14 \). For a real-world application, understanding how to simplify algebraic expressions is crucial in various fields such as engineering, economics, and computer science. For example, engineers use polynomial equations to design structures, while economists analyze functions to predict market behavior. Simplifying these expressions helps in visualizing relationships and making calculations easier! When simplifying expressions, a common mistake is neglecting to combine like terms properly or to lose track of negative signs during distribution. To prevent errors, double-check each step and consider writing out each term to ensure you are consolidating like terms correctly. Practice makes perfect, so don’t hesitate to work through various examples to sharpen your skills!