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Solving for 'n' in the Equation (3xy - 4y^2) - n = x^2 - 7xy + 8y^2
This article will guide you through the process of solving for 'n' in the given equation:
(3xy - 4y^2) - n = x^2 - 7xy + 8y^2
To isolate 'n', we need to manipulate the equation through algebraic operations.
Step 1: Combine like terms
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Group the 'xy' terms together: 3xy + 7xy = 10xy
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Group the 'y^2' terms together: -4y^2 - 8y^2 = -12y^2
The equation now becomes:
(10xy - 12y^2) - n = x^2
Step 2: Isolate 'n'
- Move all terms except 'n' to the right side of the equation:
-n = x^2 - 10xy + 12y^2
- Multiply both sides by -1 to get a positive 'n':
n = -x^2 + 10xy - 12y^2
Solution
Therefore, the solution for 'n' in the equation (3xy - 4y^2) - n = x^2 - 7xy + 8y^2 is n = -x^2 + 10xy - 12y^2.