%2B(2x%5E2%2By%5E2-2x)-(x%5E2%2B3y%5E2%2Bx).jpeg "(3x^2+2y^2-3x)+(2x^2+y^2-2x)-(x^2+3y^2+x)")
Simplifying Algebraic Expressions: A Step-by-Step Guide
This article will guide you through simplifying the algebraic expression:
(3x^2 + 2y^2 - 3x) + (2x^2 + y^2 - 2x) - (x^2 + 3y^2 + x)
Let's break down the process step-by-step:
Step 1: Remove the parentheses
Since we are adding and subtracting expressions, the parentheses don't affect the order of operations. We can simply remove them:
3x^2 + 2y^2 - 3x + 2x^2 + y^2 - 2x - x^2 - 3y^2 - x
Step 2: Group like terms
Identify terms with the same variables and exponents.
(3x^2 + 2x^2 - x^2) + (2y^2 + y^2 - 3y^2) + (-3x - 2x - x)
Step 3: Combine like terms
Add or subtract the coefficients of each group:
4x^2 + 0y^2 - 6x
Step 4: Simplify
The simplified expression is:
4x^2 - 6x
Conclusion
By applying the principles of combining like terms and removing parentheses, we successfully simplified the given algebraic expression. This process is fundamental in algebra and allows us to manipulate equations and solve problems more efficiently.