`(2x + 5)(2x - 5) = ?`

Options

A. `(4x^(2) + 25)`
B. `(4x^(2) - 25)`
C. `(4x^(2) - 10x + 25)`
D. `(4 x^(2) + 10x - 25)`

Answer

To solve the expression \((2x + 5)(2x - 5)\), we can use the identity for the difference of squares, which states that:

\[ (a + b)(a - b) = a^2 - b^2 \]

### Step-by-Step Solution:

**Step 1: Identify \(a\) and \(b\)**
In our expression, we can identify:
- \(a = 2x\)
- \(b = 5\)

**Step 2: Apply the difference of squares identity**
Using the identity, we can rewrite the expression as:
\[ (2x + 5)(2x - 5) = (2x)^2 - (5)^2 \]

**Step 3: Calculate \((2x)^2\)**
Now, we calculate \((2x)^2\):
\[ (2x)^2 = 2^2 \cdot x^2 = 4x^2 \]

**Step 4: Calculate \((5)^2\)**
Next, we calculate \((5)^2\):
\[ (5)^2 = 25 \]

**Step 5: Substitute back into the equation**
Now substitute these values back into the expression:
\[ (2x + 5)(2x - 5) = 4x^2 - 25 \]

### Final Answer:
Thus, the simplified expression is:
\[ 4x^2 - 25 \]

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