Simplify :
(5a + 5b - c)(2b - 3c)

Answer

To simplify the expression \((5a + 5b - c)(2b - 3c)\), we will use the distributive property (also known as the FOIL method for binomials). Here’s the step-by-step solution:

### Step 1: Write down the expression
We start with the expression:
\[ (5a + 5b - c)(2b - 3c) \]

### Step 2: Distribute each term in the first bracket to each term in the second bracket
We will multiply each term in the first bracket by each term in the second bracket:

1. **Multiply \(5a\) by \(2b\)**:
\[ 5a \cdot 2b = 10ab \]

2. **Multiply \(5a\) by \(-3c\)**:
\[ 5a \cdot (-3c) = -15ac \]

3. **Multiply \(5b\) by \(2b\)**:
\[ 5b \cdot 2b = 10b^2 \]

4. **Multiply \(5b\) by \(-3c\)**:
\[ 5b \cdot (-3c) = -15bc \]

5. **Multiply \(-c\) by \(2b\)**:
\[ -c \cdot 2b = -2bc \]

6. **Multiply \(-c\) by \(-3c\)**:
\[ -c \cdot (-3c) = 3c^2 \]

### Step 3: Combine all the terms
Now we combine all the results from the multiplications:
\[ 10ab - 15ac + 10b^2 - 15bc - 2bc + 3c^2 \]

### Step 4: Combine like terms
Next, we will combine the like terms:
- The \(bc\) terms: \(-15bc - 2bc = -17bc\)

So, we have:
\[ 10ab - 15ac + 10b^2 - 17bc + 3c^2 \]

### Final Answer
Thus, the simplified expression is:
\[ 10ab - 15ac + 10b^2 - 17bc + 3c^2 \]

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