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

Verified step by step guidance

1. Identify like terms in the expression: -12y, 4y, 3y, and 2y.
2. Combine the coefficients of the like terms: -12, 4, 3, and 2.
3. Add the coefficients together: (-12) + 4 + 3 + 2.
4. Simplify the sum of the coefficients to find the new coefficient for y.
5. Rewrite the expression using the simplified coefficient for y.

Key Concepts

Combining Like Terms

Combining like terms is a fundamental algebraic process where terms with the same variable and exponent are added or subtracted. In the expression -12y + 4y + 3y + 2y, the coefficients of the 'y' terms can be summed to simplify the expression. This concept is essential for simplifying algebraic expressions efficiently.

Coefficients

Coefficients are the numerical factors that multiply the variables in an algebraic expression. In the expression provided, -12, 4, 3, and 2 are the coefficients of 'y'. Understanding coefficients is crucial for performing operations like addition and subtraction in expressions involving variables.

Algebraic Expressions

An algebraic expression is a combination of numbers, variables, and arithmetic operations. The expression -12y + 4y + 3y + 2y is an example of a linear algebraic expression in one variable. Recognizing the structure of algebraic expressions is vital for simplifying and solving them.