Multiply :
`5a - 1` by 7a - 3

Answer

To multiply the expressions \(5a - 1\) and \(7a - 3\), we will use the distributive property (also known as the FOIL method for binomials). Here’s a step-by-step solution:

### Step 1: Write down the expressions
We start with the expressions:
\[ (5a - 1)(7a - 3) \]

### Step 2: Distribute the first term of the first expression
Multiply \(5a\) by each term in the second expression:
\[ 5a \cdot 7a = 35a^2 \]
\[ 5a \cdot (-3) = -15a \]

### Step 3: Distribute the second term of the first expression
Now, multiply \(-1\) by each term in the second expression:
\[ -1 \cdot 7a = -7a \]
\[ -1 \cdot (-3) = 3 \]

### Step 4: Combine all the results
Now, we combine all the results from the multiplications:
\[ 35a^2 - 15a - 7a + 3 \]

### Step 5: Combine like terms
Combine the like terms \(-15a\) and \(-7a\):
\[ -15a - 7a = -22a \]

### Final Result
Putting it all together, we get:
\[ 35a^2 - 22a + 3 \]

Thus, the product of \(5a - 1\) and \(7a - 3\) is:
\[ \boxed{35a^2 - 22a + 3} \]