If \( C=x^{2}-7 \) and \( D=2-x+9 x^{2} \), find an expression that equals \( C-2 D \) in standard form.

To find the expression that equals \( C - 2D \), we first need to substitute the given expressions for \( C \) and \( D \). Starting with: \[ C = x^{2} - 7 \] \[ D = 2 - x + 9x^{2} \] Now, we calculate \( 2D \): \[ 2D = 2(2 - x + 9x^{2}) = 4 - 2x + 18x^{2} \] Next, we can substitute \( C \) and \( 2D \) into the expression \( C - 2D \): \[ C - 2D = (x^{2} - 7) - (4 - 2x + 18x^{2}) \] Now, distribute the negative sign: \[ C - 2D = x^{2} - 7 - 4 + 2x - 18x^{2} \] Combining like terms, we have: \[ C - 2D = (x^{2} - 18x^{2}) + 2x + (-7 - 4) = -17x^{2} + 2x - 11 \] Thus, the expression that equals \( C - 2D \) in standard form is: \[ -17x^{2} + 2x - 11 \]