%E2%88%92(%E2%88%92x2%E2%88%929x%2B6)-combine-like-terms.jpeg "(−x2−3x+3)−(−x2−9x+6) Combine Like Terms")
Combining Like Terms: A Step-by-Step Guide
In mathematics, combining like terms is a fundamental operation that simplifies expressions. Let's explore how to simplify the expression (−x2−3x+3)−(−x2−9x+6) by combining like terms.
Understanding Like Terms
Like terms are terms that have the same variable(s) raised to the same power. For example:
- -x2 and -x2 are like terms because they both have the variable x raised to the power of 2.
- -3x and -9x are like terms because they both have the variable x raised to the power of 1 (which is implied).
- 3 and 6 are like terms because they are both constants (numbers without variables).
Combining Like Terms in the Expression
-
Rewrite the Expression: Start by removing the parentheses. Remember that a minus sign before a parenthesis changes the sign of each term inside the parenthesis.
( −x2 − 3x + 3) − ( −x2 − 9x + 6) becomes −x2 − 3x + 3 + x2 + 9x − 6
-
Identify Like Terms: Now, identify the like terms in the expression:
- -x2 and +x2
- -3x and +9x
- +3 and -6
-
Combine Like Terms: Combine the coefficients of each set of like terms:
- -x2 + x2 = 0
- -3x + 9x = 6x
- +3 - 6 = -3
-
Write the Simplified Expression: Combine the simplified terms:
0 + 6x - 3 = 6x - 3
Conclusion
By following these steps, we have successfully combined like terms in the expression (−x2−3x+3)−(−x2−9x+6) to obtain the simplified expression 6x - 3. Combining like terms is a crucial skill for simplifying algebraic expressions and solving equations.