`(x+a)(x-b)` = ________

Options

A. `x^(2) - (a+b)x +ab`
B. `x^(2) +(a-b) x+ ab`
C. `x^(2) - (a-b)x +ab`
D. `x^(2) +(a-b)x -ab`

Answer

To solve the expression \((x + a)(x - b)\), we will use the distributive property (also known as the FOIL method for binomials). Here’s a step-by-step breakdown of the solution:

### Step 1: Apply the Distributive Property
We will multiply each term in the first bracket by each term in the second bracket.

\[ (x + a)(x - b) = x(x - b) + a(x - b) \]

### Step 2: Distribute \(x\) in the first term
Now, we will distribute \(x\) to both terms in the second bracket:

\[ x(x - b) = x^2 - bx \]

### Step 3: Distribute \(a\) in the second term
Next, we will distribute \(a\) to both terms in the second bracket:

\[ a(x - b) = ax - ab \]

### Step 4: Combine all the terms
Now, we will combine all the terms we obtained from the previous steps:

\[ x^2 - bx + ax - ab \]

### Step 5: Rearrange the terms
We can rearrange the terms to group like terms:

\[ x^2 + (a - b)x - ab \]

### Final Answer
Thus, the expanded form of \((x + a)(x - b)\) is:

\[ x^2 + (a - b)x - ab \]

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