-3xy%3Db-5%2F3y%5E2.jpeg "(2x^3y-5xy^3) 3xy=b-5/3y^2")
Simplifying and Solving the Equation: (2x³y - 5xy³) 3xy = b - 5/3y²
This equation presents a challenge in algebra, requiring us to simplify and solve for the variable 'b'. Let's break down the process step by step:
1. Expanding the Left Side
First, we need to distribute the 3xy on the left side of the equation:
(2x³y - 5xy³) 3xy = 6x⁴y² - 15x²y⁴
2. Isolating the Variable 'b'
Our goal is to isolate 'b'. To do this, we need to move all terms containing 'b' to one side of the equation and all other terms to the other side:
6x⁴y² - 15x²y⁴ = b - 5/3y²
Adding 5/3y² to both sides:
6x⁴y² - 15x²y⁴ + 5/3y² = b
3. Simplifying the Expression
We can simplify the expression on the left side by finding a common denominator for the fractions:
(18x⁴y²/3 - 45x²y⁴/3 + 5/3y²) = b
Combining the terms:
(18x⁴y² - 45x²y⁴ + 5y²)/3 = b
Conclusion
Therefore, the solution for 'b' in terms of x and y is:
b = (18x⁴y² - 45x²y⁴ + 5y²)/3
This equation represents the relationship between the variables b, x, and y, given the initial equation. It's important to note that this is a general solution and the specific values of b will depend on the specific values of x and y.