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One of the first steps in subtracting polynomials is distributing the negative sign into the second polynomial. This step involves using the distributive property. The distributive property states that a term outside of parentheses affects each term inside the parentheses. In this case, when you see a subtraction sign in front of a polynomial, it acts like a negative one multiplying the entire expression.
For instance, if you start with the expression \(x - (7x + 9)\), you need to distribute the negative sign to each term inside the parenthesis. This means applying the operations:\(-1 \cdot 7x = -7x\) and \(-1 \cdot 9 = -9\). By doing so, the expression transforms from \(x - (7x + 9)\) to \(x - 7x - 9\). This step is crucial for correctly setting up the polynomial subtraction.

Understanding like terms is important when working with polynomials. Like terms are terms that have the same variable raised to the same power. In order to add, subtract, or combine them, you must first identify which terms are alike.

• For terms with variables, both the variable and the exponent must match. For example, \(x\) and \(-7x\) are like terms because they both have the variable 'x' raised to the first power.
• Constant terms are considered like terms with other constants, such as \(-2\) and \(-9\).

When dealing with the expression from our example, like terms would be \(x - 7x\) and \(-2 - 9\). Identifying like terms allows you to combine them in the next step.

After identifying and grouping like terms, the next step is to simplify the expression. Simplification means performing the actual addition or subtraction of the coefficients of like terms.
Taking the example expression \(x - 7x - 2 - 9\):

• First, simplify the variable terms: \(x - 7x\). Here you subtract the coefficients (1 - 7) which results in \(-6x\).
• Next, simplify the constant terms: \(-2 - 9\). Add these together (as they are both negative) to get \(-11\).

The final simplified expression becomes \(-6x - 11\). By following these simplification steps, you can ensure that your polynomial subtraction is done correctly, leading to a neat and accurate result.