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In algebra, one of the key steps in adding polynomials is to identify 'like terms'. Like terms are terms that contain the same variable raised to the same power. For example, in the polynomials \(14m - 9\) and \(12m + 2\), the terms \(14m\) and \(12m\) are like terms because they both contain the variable \(m\) raised to the same power (which is 1 in this case). Similarly, the constants \(-9\) and \(+2\) are like terms because they are both just numbers without any variable.

When identifying like terms:

• Look for terms with the same variable and the same exponent.
• Constants (numbers without variables) are also considered like terms.

By correctly identifying these like terms, you set the groundwork for the next steps in combining and simplifying the expressions.

Once you've identified the like terms, the next step is to combine them. This involves adding or subtracting the coefficients of the like terms. The coefficient is the number in front of the variable. For instance, in the term \(14m\), 14 is the coefficient.

Let's look at our example:

• We have the like terms \(14m\) and \(12m\). To combine these, we simply add their coefficients: \(14 + 12 = 26\). So, \(14m + 12m = 26m\).
• Next, we have the constants \(-9\) and \(+2\). Adding these gives us: \(-9 + 2 = -7\).

Combining coefficients helps streamline the expression and makes the polynomial much easier to work with for further operations.

After combining the like terms, the final step in adding polynomials is to simplify the expression. This means writing the polynomial in the simplest form by combining all the like terms and presenting the final result in an organized way.

Looking back at our example, after combining the coefficients, we have the terms \(26m\) and \(-7\). These cannot be combined any further because they are not like terms. Thus, the simplified form of the polynomial is:

• \(26m - 7\)

By simplifying the expression, you ensure that the polynomial is in its most reduced and understandable form. This is useful not just for ease of reading, but also for carrying out further mathematical operations such as additional additions, subtractions, factorizations, or solving equations.