Combining Like Terms: A StepbyStep 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.