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Simplify the expression: 2(x)² * (1/4)xy * 8x / ((3x * 4y)⁻¹)⁻²

Mathematics

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Answer

z2+x2+4x−4y−18z2(x−2y−9z)2\dfrac{z^{2}+x^{2}+4x-4y-18z}{2(x-2y-9z)^{2}}

Step-by-step solution

6 steps

  1. The given expression is

    2(z2+x2+4x−4y−18z)(2x−4y−18z)2.\frac{2(z^{2} + x^{2} + 4x - 4y - 18z)}{(2x - 4y - 18z)^{2}}.

  2. Factor out the 2 from the base of the denominator

    2x−4y−18z=2(x−2y−9z).2x - 4y - 18z = 2(x - 2y - 9z).

  3. Square the factored form

    (2x−4y−18z)2=[2(x−2y−9z)]2=4(x−2y−9z)2.(2x - 4y - 18z)^{2} = [2(x - 2y - 9z)]^{2} = 4(x - 2y - 9z)^{2}.

  4. Substitute into the original expression

    2(z2+x2+4x−4y−18z)4(x−2y−9z)2.\frac{2(z^{2} + x^{2} + 4x - 4y - 18z)}{4(x - 2y - 9z)^{2}}.

  5. Simplify the constant coefficient

    24(z2+x2+4x−4y−18z)⋅1(x−2y−9z)2=12⋅z2+x2+4x−4y−18z(x−2y−9z)2.\frac{2}{4} (z^{2} + x^{2} + 4x - 4y - 18z) \cdot \frac{1}{(x - 2y - 9z)^{2}} = \frac{1}{2} \cdot \frac{z^{2} + x^{2} + 4x - 4y - 18z}{(x - 2y - 9z)^{2}}.

  6. Write in single fraction form

    z2+x2+4x−4y−18z2(x−2y−9z)2.\frac{z^{2} + x^{2} + 4x - 4y - 18z}{2(x - 2y - 9z)^{2}}.

    \dfrac{z^{2}+x^{2}+4x-4y-18z}{2(x-2y-9z)^{2}}

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