Simplifying algebraic expressions involves combining like terms to write the expression in its most compact form. Like terms have the same variable raised to the same power (e.g., $3x$ and $-5x$ are like terms, but $3x$ and $3x^2$ are not). To simplify, you add or subtract the coefficients of like terms, keeping the variable and exponent the same. Remember the distributive property when dealing with parentheses: $a(b+c) = ab + ac$. Simplifying expressions makes them easier to work with in solving equations and other algebraic manipulations.
Match each term with its definition:
| Term | Definition |
|---|---|
| 1. Variable | A. A value that does not change |
| 2. Coefficient | B. A symbol representing an unknown quantity |
| 3. Constant | C. Terms that have the same variable(s) raised to the same power(s) |
| 4. Like Terms | D. The number multiplied by a variable |
| 5. Expression | E. A mathematical phrase containing numbers, variables, and operations |
Complete the paragraph with the correct terms:
When simplifying an algebraic __________, we combine __________. Like terms have the same __________ raised to the same __________. For example, in the expression $5x + 3y - 2x + y$, the like terms are $5x$ and __________, and $3y$ and __________. Combining these gives us __________ + __________.
Explain in your own words why it is important to simplify algebraic expressions before solving an equation.
Please log in to post your answer.
Log InEarn 2 Points for answering. If your answer is selected as the best, you'll get +20 Points! 🚀