`121-16a^(2)b^(2)` = ________

Options

A. `(11+16ab)(11-ab)`
B. `(11+16ab) (11+ab)`
C. `(11-4ab)(11+4ab)`
D. `(11-4ab)(11-4ab)`

Answer

To factor the expression \(121 - 16a^2b^2\), we can follow these steps:

### Step 1: Identify the expression
We start with the expression:
\[ 121 - 16a^2b^2 \]

### Step 2: Recognize the form of a difference of squares
Notice that \(121\) can be expressed as \(11^2\) and \(16a^2b^2\) can be expressed as \((4ab)^2\). Therefore, we can rewrite the expression as:
\[ 11^2 - (4ab)^2 \]

### Step 3: Apply the difference of squares formula
We can use the difference of squares formula, which states that \(x^2 - y^2 = (x + y)(x - y)\). Here, \(x = 11\) and \(y = 4ab\). Applying the formula gives us:
\[ (11 + 4ab)(11 - 4ab) \]

### Step 4: Write the final factored form
Thus, the factored form of the expression \(121 - 16a^2b^2\) is:
\[ (11 + 4ab)(11 - 4ab) \]

### Final Answer:
\[ 121 - 16a^2b^2 = (11 + 4ab)(11 - 4ab) \]

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