: -n – 10n – 9n -3
The Correct Answer and Explanation is:
Simplified Expression:
−n−10n−9n−3=−20n−3-n – 10n – 9n – 3 = -20n – 3
Explanation:
To simplify the expression −n−10n−9n−3-n – 10n – 9n – 3, we need to combine like terms. Like terms are terms that have the same variables raised to the same power. In this expression, the like terms are the ones involving the variable nn: −n-n, −10n-10n, and −9n-9n. The constant −3-3 does not have a variable, so it will remain separate from the variable terms.
Let’s go step by step:
- Identify like terms:
- Variable terms: −n-n, −10n-10n, and −9n-9n
- Constant term: −3-3
- Combine variable terms:
- Start by understanding that −n-n is the same as −1n-1n.
- So we are really adding: −1n−10n−9n-1n – 10n – 9n
- Now combine them: −1n−10n=−11n-1n – 10n = -11n −11n−9n=−20n-11n – 9n = -20n
- Bring down the constant term:
- After combining the variable terms into −20n-20n, we include the constant term −3-3.
- Final simplified expression: −20n−3-20n – 3
This expression cannot be simplified further because there are no more like terms to combine. One part of the expression contains a variable (−20n-20n) and the other part is a constant (−3-3).
Simplifying algebraic expressions by combining like terms is a foundational algebra skill. It helps us write expressions in their simplest form and is crucial for solving equations, factoring, and performing other algebraic operations. Always group similar terms and be mindful of negative signs, as they play a key role in correct simplification.
