Simplify this expression by collecting like terms:15ab + 5bc − 6ac + 9 + 14ac − 5 − 5bc

1. Break Down the Problem

We need to simplify the expression $15ab + 5bc - 6ac + 9 + 14ac - 5 - 5bc$ by collecting like terms.

2. Relevant Concepts

Like terms are terms that have the same variable(s) raised to the same power. We will group these terms together.

3. Analysis and Detail

Let's identify and group the like terms in the expression:

• Terms with $ab$: $15ab$
• Terms with $bc$: $5bc - 5bc = 0$
• Terms with $ac$: $-6ac + 14ac = 8ac$
• Constant terms: $9 - 5 = 4$

Now we can write the simplified expression by combining these groups.

4. Verify and Summarize

Combining all the like terms, we have:

• From $ab$: $15ab$
• From $bc$: $0$
• From $ac$: $8ac$
• Constant: $4$

Final Answer

The simplified expression is: $15ab + 8ac + 4$