Questions: Simplify the following polynomial by combining any like terms. 2 a b-4 a+9 a b-2 a 2 a b-4 a+9 a b-2 a=

Transcript text: Simplify the following polynomial by combining any like terms. \[ \begin{array}{l} 2 a b-4 a+9 a b-2 a \\ 2 a b-4 a+9 a b-2 a= \end{array} \]

Solution

Solution Steps

To simplify the polynomial, we need to combine like terms. Like terms are terms that have the same variables raised to the same powers. In this expression, we will group and combine the terms involving \(ab\) and the terms involving \(a\).

Step 1: Combine Like Terms

We start with the polynomial expression: \[ 2ab - 4a + 9ab - 2a \] We can group the like terms: \[ (2ab + 9ab) + (-4a - 2a) \] This simplifies to: \[ 11ab - 6a \]

Step 2: Factor the Expression

Next, we can factor out the common term \(a\) from the expression: \[ 11ab - 6a = a(11b - 6) \]