Multiply `(5x-5)` by `(3x+5)`

Answer

To multiply the expressions \( (5x - 5) \) and \( (3x + 5) \), we will use the distributive property (also known as the FOIL method for binomials). Here’s a step-by-step solution:

### Step 1: Distribute the first term of the first expression
Multiply \( 5x \) by each term in the second expression \( (3x + 5) \):
\[ 5x \cdot 3x + 5x \cdot 5 \]
Calculating these gives:
\[ 15x^2 + 25x \]

### Step 2: Distribute the second term of the first expression
Now, multiply \( -5 \) by each term in the second expression \( (3x + 5) \):
\[ -5 \cdot 3x + (-5) \cdot 5 \]
Calculating these gives:
\[ -15x - 25 \]

### Step 3: Combine all the results
Now, we combine all the terms from Step 1 and Step 2:
\[ 15x^2 + 25x - 15x - 25 \]

### Step 4: Simplify the expression
Combine like terms:
\[ 15x^2 + (25x - 15x) - 25 \]
This simplifies to:
\[ 15x^2 + 10x - 25 \]

### Final Answer:
The product of \( (5x - 5) \) and \( (3x + 5) \) is:
\[ 15x^2 + 10x - 25 \]

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