4x2 - y2/8x2 + 10xy + 3y2 * 4x2 - 9xy - 9y2/2x2 - 5xy - 3y2

4x^2 - y^2/8x^2 + 10xy + 3y^2 * 4x^2 - 9xy - 9y^2/2x^2 - 5xy - 3y^2

Steps

Group like terms

= 4x^2 + 3 * 4x^2y^2 + 10xy - 9xy - 5xy - y^2/8x^2 - 9y^2/2x^2 - 3y^2

10xy - 9xy - 5xy = - 4xy

= 4x^2 + 3 * 4x^2y^2 - 4xy - y^2/8x^2 - 9y^2/2x^2 - 3y^2

Then, multiply the numbers: 3 * 4 = 12

Then, convert element to fraction:

4x^2 = 4x^2/1

12x^2y^2 = 12x^2y^2/1

4xy = 4xy/1

3y^2 = 3y^2/1

Which then equals:

-y^2/8x^2 - 9y^2/2x^2 + 4x^2/1 + 12x^2y^2/1 - 4xy/1 - 3y^2/1

Then, find the least common denominator (LCD) for the equation: 8x^2

Then, adjust fractions based on the LCD

= - y^2/8x^2 - 9y^2 * 4/8x^2 + 4x^2 * 8x^2/8x^2 + 12x^2y^2 * 8x^2/8x^2 -

4xy * 8x^2/8x^2 - 3y^2 * 8x^2/8x^2

Add the numerators all together: - 37y^2 + 32x^4 + 96x^4y^2 - 32x^3y - 24x^2y^2

= - 37y^2 + 32x^4 + 96x^4y^2 - 32x^3y - 24x^2y^2/8x^2