Find each of the following products :
`(3m - 4n) xx (2m - 3n)`

Answer

To find the product of the algebraic expressions \( (3m - 4n) \) and \( (2m - 3n) \), 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 expression
We start with the expression:
\[ (3m - 4n)(2m - 3n) \]

### Step 2: Distribute the first term of the first expression
Multiply \( 3m \) by each term in the second expression:
\[ 3m \cdot 2m = 6m^2 \]
\[ 3m \cdot (-3n) = -9mn \]

### Step 3: Distribute the second term of the first expression
Now, multiply \( -4n \) by each term in the second expression:
\[ -4n \cdot 2m = -8mn \]
\[ -4n \cdot (-3n) = 12n^2 \]

### Step 4: Combine all the products
Now, we combine all the results from the previous steps:
\[ 6m^2 - 9mn - 8mn + 12n^2 \]

### Step 5: Combine like terms
Combine the like terms \( -9mn \) and \( -8mn \):
\[ 6m^2 - 17mn + 12n^2 \]

### Final Answer
Thus, the product of the expressions is:
\[ 6m^2 - 17mn + 12n^2 \]

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