g) \( 2[2 y-3(y+1)]+3[y+2(3 y-4)] \)

To simplify the expression: \[ 2[2y - 3(y + 1)] + 3[y + 2(3y - 4)] \] Let's break it down step by step. ### Step 1: Expand Inside the Brackets 1. **First Bracket:** \[ 2[2y - 3(y + 1)] \] Expand the terms inside: \[ 2y - 3(y + 1) = 2y - 3y - 3 = -y - 3 \] Multiply by 2: \[ 2(-y - 3) = -2y - 6 \] 2. **Second Bracket:** \[ 3[y + 2(3y - 4)] \] Expand the terms inside: \[ 2(3y - 4) = 6y - 8 \] Add \( y \): \[ y + 6y - 8 = 7y - 8 \] Multiply by 3: \[ 3(7y - 8) = 21y - 24 \] ### Step 2: Combine the Expanded Terms Now, add the results from both brackets: \[ -2y - 6 + 21y - 24 \] Combine like terms: \[ (-2y + 21y) + (-6 - 24) = 19y - 30 \] ### **Final Simplified Expression:** \[ 19y - 30 \]