Fill in the blanks.
`(x+a)(x+b)`= ______

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 the step-by-step solution:

### Step 1: Distribute the first term
We start by multiplying the first term in the first bracket by each term in the second bracket:
\[ x \cdot (x + b) = x^2 + bx \]

### Step 2: Distribute the second term
Next, we multiply the second term in the first bracket by each term in the second bracket:
\[ a \cdot (x + b) = ax + ab \]

### Step 3: Combine all the terms
Now, we combine all the terms we obtained from the previous steps:
\[ x^2 + bx + ax + ab \]

### Step 4: Combine like terms
The terms \(bx\) and \(ax\) are like terms, so we can combine them:
\[ x^2 + (a + b)x + ab \]

### Final Answer
Thus, the expression \((x + a)(x + b)\) expands to:
\[ x^2 + (a + b)x + ab \]

### Fill in the blank:
So, the answer to fill in the blank is:
\[ x^2 + (a + b)x + ab \]

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