Final answer:
When combining like terms in the expression 2ab - 4a + 5b + 6ab, you end up with three terms: 8ab, -4a, and 5b. This is because 2ab and 6ab are like terms and their coefficients can be added together.
Step-by-step explanation:
When you combine like terms in the expression 2ab - 4a + 5b + 6ab, you look for terms that have the same variables raised to the same powers. Here, 2ab and 6ab are like terms because they both contain the variable a to the first power and variable b to the first power. You can combine these by adding their coefficients to get 8ab. The other terms, -4a and 5b, do not have like terms, so they remain unaltered.
By combining like terms, the expression simplifies to 8ab - 4a + 5b. Therefore, there are three terms after combining like terms. This demonstrates the commutative property of addition, where A + B = B + A, which holds true for the combining of like terms as well.
It is important to eliminate terms wherever possible to simplify the algebra. This means combining all like terms to reduce the expression to its simplest form. Furthermore, you should always check the answer to ensure it is reasonable and correctly simplified.