Find the products for the following :
(x-5) ( x + 6)

Answer

To find the product of the expression (x - 5)(x + 6), we will use the distributive property (also known as the FOIL method for binomials). Here’s the step-by-step solution:

### Step 1: Write down the expression
We start with the expression:
\[ (x - 5)(x + 6) \]

### Step 2: Apply the distributive property
We will distribute each term in the first bracket by each term in the second bracket. This means we will multiply \(x\) by both \(x\) and \(6\), and then \(-5\) by both \(x\) and \(6\).

\[ = x \cdot x + x \cdot 6 - 5 \cdot x - 5 \cdot 6 \]

### Step 3: Perform the multiplications
Now we will calculate each multiplication:
- \(x \cdot x = x^2\)
- \(x \cdot 6 = 6x\)
- \(-5 \cdot x = -5x\)
- \(-5 \cdot 6 = -30\)

Putting these together, we have:
\[ = x^2 + 6x - 5x - 30 \]

### Step 4: Combine like terms
Now we combine the like terms \(6x\) and \(-5x\):
\[ = x^2 + (6x - 5x) - 30 \]
\[ = x^2 + 1x - 30 \]

### Step 5: Write the final expression
Thus, the final product of the expression is:
\[ x^2 + x - 30 \]