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28 March, 13:59

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

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  1. 28 March, 14:04
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    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
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