Multiply :
`12a + 5b` by `7a - b`

Answer

To multiply the algebraic expressions \(12a + 5b\) and \(7a - b\), we will use the distributive property (also known as the FOIL method for binomials). Here’s how to do it step by step:

### Step 1: Distribute the first term of the first expression
Multiply \(12a\) by each term in the second expression \(7a - b\):
\[ 12a \cdot 7a = 84a^2 \]
\[ 12a \cdot (-b) = -12ab \]

### Step 2: Distribute the second term of the first expression
Now multiply \(5b\) by each term in the second expression \(7a - b\):
\[ 5b \cdot 7a = 35ab \]
\[ 5b \cdot (-b) = -5b^2 \]

### Step 3: Combine all the terms
Now, combine all the results from Step 1 and Step 2:
\[ 84a^2 - 12ab + 35ab - 5b^2 \]

### Step 4: Combine like terms
Now, combine the like terms \(-12ab\) and \(35ab\):
\[ 84a^2 + (35ab - 12ab) - 5b^2 = 84a^2 + 23ab - 5b^2 \]

### Final Answer
Thus, the product of \(12a + 5b\) and \(7a - b\) is:
\[ \boxed{84a^2 + 23ab - 5b^2} \]

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