Multiply :
`x + 4` by x - 5

Answer

To multiply the expressions \( (x + 4) \) and \( (x - 5) \), we will use the distributive property (also known as the FOIL method for binomials). Here are the steps:

### Step 1: Write down the expression
We start with the expression:
\[ (x + 4)(x - 5) \]

### Step 2: Apply the distributive property
We will multiply each term in the first expression by each term in the second expression:
1. Multiply \( x \) by \( x \)
2. Multiply \( x \) by \( -5 \)
3. Multiply \( 4 \) by \( x \)
4. Multiply \( 4 \) by \( -5 \)

### Step 3: Perform the multiplications
1. \( x \cdot x = x^2 \)
2. \( x \cdot (-5) = -5x \)
3. \( 4 \cdot x = 4x \)
4. \( 4 \cdot (-5) = -20 \)

### Step 4: Combine all the results
Now, we combine all these results:
\[ x^2 - 5x + 4x - 20 \]

### Step 5: Combine like terms
Next, we combine the like terms \(-5x\) and \(4x\):
\[ -5x + 4x = -1x \text{ or } -x \]

So, we have:
\[ x^2 - x - 20 \]

### Final Answer
Thus, the product of \( (x + 4) \) and \( (x - 5) \) is:
\[ \boxed{x^2 - x - 20} \]

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