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

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UpStudy AI · Accepted Answer

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:**

$$
19y - 30
$$
The simplified expression is $$ 19y - 30 $$.

g)

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