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(3xy-4y^2)-n=x^2-7xy+8y^2

2 min read Jun 16, 2024
(3xy-4y^2)-n=x^2-7xy+8y^2

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

  • Group the 'xy' terms together: 3xy + 7xy = 10xy

  • 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.

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