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