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Simplify : (px - q)(px + q)...

Simplify :
(px - q)(px + q)

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To simplify the expression \((px - q)(px + q)\), we can use the difference of squares formula, which states that: \[ (a - b)(a + b) = a^2 - b^2 \] ### Step-by-Step Solution: 1. **Identify \(a\) and \(b\)**: - In our case, we can let \(a = px\) and \(b = q\). 2. **Apply the difference of squares formula**: - According to the formula, we can rewrite the expression: \[ (px - q)(px + q) = (a - b)(a + b) = a^2 - b^2 \] 3. **Substitute \(a\) and \(b\)**: - Substitute back \(a\) and \(b\) into the formula: \[ = (px)^2 - q^2 \] 4. **Calculate \(a^2\) and \(b^2\)**: - Calculate \((px)^2\): \[ (px)^2 = p^2x^2 \] - Thus, we have: \[ = p^2x^2 - q^2 \] 5. **Final Result**: - Therefore, the simplified expression is: \[ p^2x^2 - q^2 \] ### Final Answer: \[ p^2x^2 - q^2 \] ---
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