Find each of the following products :
`(4x + 9) xx (x - 6)`

Answer

To find the product of the algebraic expression \((4x + 9)(x - 6)\), we will use the distributive property, also known as the FOIL method (First, Outside, Inside, Last). Here are the steps:

### Step 1: Distribute \(4x\) to both terms in the second bracket \((x - 6)\)
\[ 4x \cdot x + 4x \cdot (-6) \]
This gives us:
\[ 4x^2 - 24x \]

### Step 2: Distribute \(9\) to both terms in the second bracket \((x - 6)\)
\[ 9 \cdot x + 9 \cdot (-6) \]
This gives us:
\[ 9x - 54 \]

### Step 3: Combine all the terms from Steps 1 and 2
Now, we combine the results from the two distributions:
\[ 4x^2 - 24x + 9x - 54 \]

### Step 4: Combine like terms
Now, we combine the like terms \(-24x\) and \(9x\):
\[ 4x^2 + (-24x + 9x) - 54 \]
This simplifies to:
\[ 4x^2 - 15x - 54 \]

### Final Answer
Thus, the product of \((4x + 9)(x - 6)\) is:
\[ \boxed{4x^2 - 15x - 54} \]

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