Combine like terms: $3 x^2+2 x y-4 x+5 y+3 x y-x^2$
Answer (1)
Identify like terms.
Combine the x 2 terms: 3 x 2 − x 2 = 2 x 2 .
Combine the x y terms: 2 x y + 3 x y = 5 x y .
Write the simplified expression: 2 x 2 + 5 x y − 4 x + 5 y .
Explanation
Understanding the Problem We are asked to combine like terms in the expression 3 x 2 + 2 x y − 4 x + 5 y + 3 x y − x 2 . This involves identifying terms with the same variable factors and adding or subtracting their coefficients.
Identifying Like Terms First, let's identify the like terms. We have x 2 terms, x y terms, x terms, and y terms.
Combining x^2 Terms Now, let's combine the x 2 terms: 3 x 2 − x 2 = ( 3 − 1 ) x 2 = 2 x 2 .
Combining xy Terms Next, let's combine the x y terms: 2 x y + 3 x y = ( 2 + 3 ) x y = 5 x y .
Identifying Remaining Terms The remaining terms, − 4 x and 5 y , do not have any like terms to combine with.
Writing the Simplified Expression Finally, we write the simplified expression by combining the results from the previous steps: 2 x 2 + 5 x y − 4 x + 5 y .
Final Answer Therefore, the simplified expression is 2 x 2 + 5 x y − 4 x + 5 y .
Examples
Combining like terms is a fundamental skill in algebra. For example, if you are calculating the area of a garden that has different sections with similar dimensions, you can use this skill to simplify the expression for the total area. Suppose you have two rectangular sections with area x 2 , five sections with area x y , a path taking up area 4 x , and a flower bed with area 5 y . The total area can be expressed as 2 x 2 + 5 x y − 4 x + 5 y . This skill is also useful in physics when dealing with forces or energies that have similar components.
