(a) \( 3 x+2 y+4+6 x+5 y+9 \) (b) \( 8 m+2 n+5-3 m-2 n+3 \) (c) \( 12 p+24 q-5-5 q-12 p-5 \)

Sure, let's simplify each of the given algebraic expressions by combining like terms. --- ### **(a) \( 3x + 2y + 4 + 6x + 5y + 9 \)** **Step 1: Identify like terms.** - **Terms with \( x \):** \( 3x \) and \( 6x \) - **Terms with \( y \):** \( 2y \) and \( 5y \) - **Constant terms:** \( 4 \) and \( 9 \) **Step 2: Combine the like terms.** - \( 3x + 6x = 9x \) - \( 2y + 5y = 7y \) - \( 4 + 9 = 13 \) **Simplified Expression:** \[ 9x + 7y + 13 \] --- ### **(b) \( 8m + 2n + 5 - 3m - 2n + 3 \)** **Step 1: Identify like terms.** - **Terms with \( m \):** \( 8m \) and \( -3m \) - **Terms with \( n \):** \( 2n \) and \( -2n \) - **Constant terms:** \( 5 \) and \( 3 \) **Step 2: Combine the like terms.** - \( 8m - 3m = 5m \) - \( 2n - 2n = 0n \) (These terms cancel each other out.) - \( 5 + 3 = 8 \) **Simplified Expression:** \[ 5m + 8 \] *Note:* Since the \( n \) terms cancel out, they do not appear in the final expression. --- ### **(c) \( 12p + 24q - 5 - 5q - 12p - 5 \)** **Step 1: Identify like terms.** - **Terms with \( p \):** \( 12p \) and \( -12p \) - **Terms with \( q \):** \( 24q \) and \( -5q \) - **Constant terms:** \( -5 \) and \( -5 \) **Step 2: Combine the like terms.** - \( 12p - 12p = 0p \) (These terms cancel each other out.) - \( 24q - 5q = 19q \) - \( -5 - 5 = -10 \) **Simplified Expression:** \[ 19q - 10 \] *Note:* Since the \( p \) terms cancel out, they do not appear in the final expression. --- **Summary of Simplified Expressions:** - **(a)** \( 9x + 7y + 13 \) - **(b)** \( 5m + 8 \) - **(c)** \( 19q - 10 \)