Score: \( 2 \pi \) Penalty: none Question If \( C=x^{2}+7 x+5 \) and \( D=x^{2}-8 \), find an expression that equals \( 3 C-2 D \) in standard form. Answer Attempt 1 out of 2 Whow Examples Video Submit Answer

Simplify the expression by following steps: - step0: Rearrange the terms: \(2\left(x^{2}-8\right)\) - step1: Rearrange the terms: \(2x^{2}-16\) Expand the expression \( 3*(x^{2}+7*x+5) \) Simplify the expression by following steps: - step0: Rearrange the terms: \(3\left(x^{2}+7x+5\right)\) - step1: Rearrange the terms: \(3x^{2}+21x+15\) Expand the expression \( 3x^{2}+21x+15-(2x^{2}-16) \) Simplify the expression by following steps: - step0: Calculate: \(3x^{2}+21x+15-\left(2x^{2}-16\right)\) - step1: Remove the parentheses: \(3x^{2}+21x+15-2x^{2}+16\) - step2: Subtract the terms: \(x^{2}+21x+31\) To find the expression that equals \( 3C - 2D \) in standard form, we start with the given expressions for \( C \) and \( D \): 1. **Given:** - \( C = x^{2} + 7x + 5 \) - \( D = x^{2} - 8 \) 2. **Calculate \( 3C \):** \[ 3C = 3(x^{2} + 7x + 5) = 3x^{2} + 21x + 15 \] 3. **Calculate \( 2D \):** \[ 2D = 2(x^{2} - 8) = 2x^{2} - 16 \] 4. **Now, substitute these into the expression \( 3C - 2D \):** \[ 3C - 2D = (3x^{2} + 21x + 15) - (2x^{2} - 16) \] 5. **Simplify the expression:** \[ 3C - 2D = 3x^{2} + 21x + 15 - 2x^{2} + 16 \] \[ = (3x^{2} - 2x^{2}) + 21x + (15 + 16) \] \[ = x^{2} + 21x + 31 \] Thus, the expression that equals \( 3C - 2D \) in standard form is: \[ \boxed{x^{2} + 21x + 31} \]