-%E2%80%93-(%E2%80%937x2y3-%2B-6xy2-%E2%80%93-2y).jpeg "(4x2y3 + 2xy2 – 2y) – (–7x2y3 + 6xy2 – 2y)")
Simplifying Algebraic Expressions: (4x²y³ + 2xy² – 2y) – (–7x²y³ + 6xy² – 2y)
In algebra, simplifying expressions involves combining like terms to create a more concise representation. Let's break down the steps to simplify the expression: (4x²y³ + 2xy² – 2y) – (–7x²y³ + 6xy² – 2y).
1. Distributing the Negative Sign
The first step is to distribute the negative sign in front of the second set of parentheses:
(4x²y³ + 2xy² – 2y) + (7x²y³ – 6xy² + 2y)
2. Identifying Like Terms
Now, we identify terms that have the same variable and exponent combination. These are called like terms:
- x²y³: 4x²y³ and 7x²y³
- xy²: 2xy² and -6xy²
- y: -2y and 2y
3. Combining Like Terms
We combine the coefficients of like terms while keeping the variables and exponents the same:
- x²y³: 4x²y³ + 7x²y³ = 11x²y³
- xy²: 2xy² - 6xy² = -4xy²
- y: -2y + 2y = 0
4. The Simplified Expression
Finally, we put the combined terms together:
11x²y³ - 4xy²
Therefore, the simplified form of the expression (4x²y³ + 2xy² – 2y) – (–7x²y³ + 6xy² – 2y) is 11x²y³ - 4xy².