Simplify each expression. See Example 8.-6p + 5 - 4p + 6 + 11p

Verified step by step guidance

1. Identify and group the like terms in the expression. The terms involving the variable \(p\) are \(-6p\), \(-4p\), and \$11p\(. The constant terms are \)5\( and \)6$.
2. Combine the coefficients of the \(p\) terms by adding them together: \(-6p + (-4p) + 11p\).
3. Add the constant terms together: \$5 + 6$.
4. Write the simplified expression by combining the results from the previous two steps: the sum of the \(p\) terms plus the sum of the constants.
5. Express the final simplified form as \(ap + b\), where \(a\) and \(b\) are the sums you calculated in the previous steps.

Key Concepts

Combining Like Terms

Combining like terms involves adding or subtracting terms that have the same variable raised to the same power. In this expression, terms with the variable 'p' can be combined separately from constant terms to simplify the expression.

Understanding Variables and Constants

Variables represent unknown values and can be combined only with like variables, while constants are fixed numbers. Recognizing which terms are variables and which are constants helps in correctly simplifying algebraic expressions.

Simplification of Algebraic Expressions

Simplification means rewriting an expression in its simplest form by performing all possible operations. This includes combining like terms and reducing the expression to the fewest terms without changing its value.