Simplify each expression. See Example 8. -12y + 4y + 3y + 2y

Verified step by step guidance

1. Identify the like terms in the expression: all terms have the variable \(y\), so they can be combined.
2. Write the expression grouping the coefficients of \(y\): \((-12 + 4 + 3 + 2) y\).
3. Add the coefficients inside the parentheses: calculate \(-12 + 4 + 3 + 2\) step by step.
4. Once the sum of the coefficients is found, multiply it by \(y\) to write the simplified expression.
5. Write the final simplified expression as the product of the resulting coefficient and \(y\).

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, all terms contain the variable y, so their coefficients can be summed directly to simplify the expression.

Coefficients in Algebraic Expressions

Coefficients are the numerical factors multiplied by variables in algebraic terms. Understanding how to add and subtract these coefficients correctly is essential for simplifying expressions involving multiple terms with the same variable.

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 a single term or fewer terms for easier interpretation and further calculation.