This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
ScanSolve AI Answer
Step 1: The given expression is 2(z^2 + x^2 + 4x - 4y - 18z)(2x - 4y - 18z)^2. Step 2: Factor out the 2 from the base of the denominator: 2x - 4y - 18z = 2(x - 2y - 9z). Step 3: Square the factored form: (2x - 4y - 18z)^2 = [2(x - 2y - 9z)]^2 = 4(x - 2y - 9z)^2. Step 4: Substitute into the original expression: 2(z^2 + x^2 + 4x - 4y - 18z)4(x - 2y - 9z)^2. Step 5: Simplify the constant coefficient: (2)/(4) (z^2 + x^2 + 4x - 4y - 18z) · (1)/((x - 2y - 9z)^2) = (1)/(2) · z^2 + x^2 + 4x - 4y - 18z(x - 2y - 9z)^2. Step 6: Write in single fraction form: z^2 + x^2 + 4x - 4y - 18z2(x - 2y - 9z)^2. z^2+x^2+4x-4y-18z2(x-2y-9z)^2