Score: \( 8 / 10 \) Penalty: none Question If \( D=1+4 p-6 p^{2} \) and \( C=1-p \), find an expression that equals \( 2 D-3 C \) in standard form. Answer Attempt 1 out of 2 Show Examples Watch video

To find an expression that equals \( 2D - 3C \) in standard form, follow these steps: ### Given: \[ D = 1 + 4p - 6p^{2} \] \[ C = 1 - p \] ### Step 1: Substitute \( D \) and \( C \) into \( 2D - 3C \) \[ 2D - 3C = 2(1 + 4p - 6p^{2}) - 3(1 - p) \] ### Step 2: Distribute the constants into each expression \[ = 2 \cdot 1 + 2 \cdot 4p + 2 \cdot (-6p^{2}) - 3 \cdot 1 + 3 \cdot p \] \[ = 2 + 8p - 12p^{2} - 3 + 3p \] ### Step 3: Combine like terms - **Constant terms:** \( 2 - 3 = -1 \) - **\( p \) terms:** \( 8p + 3p = 11p \) - **\( p^{2} \) terms:** \( -12p^{2} \) ### Step 4: Write the expression in standard form \[ 2D - 3C = -12p^{2} + 11p - 1 \] ### Final Answer: \[ 2D - 3C = -12p^{2} + 11p - 1 \]