$(78.95)^2 - (43.35)^2 = $ $x$

### Concept & Formula This problem tests your ability to simplify calculations using the difference of squares identity. $$a^2 - b^2 = (a - b)(a + b)$$ ### Step-by-Step Solution * Let $a = 78.95$ and $b = 43.35$. * Apply the difference of squares formula: $(78.95)^2 - (43.35)^2 = (78.95 - 43.35)(78.95 + 43.35)$. * Calculate the difference $(a - b)$: $$78.95 - 43.35 = 35.60$$ * Calculate the sum $(a + b)$: $$78.95 + 43.35 = 122.30$$ * Multiply the two results: $$35.60 \times 122.30$$ * To simplify multiplication, you can treat it as $35.6 \times 122.3 = 4353.88$. ### Exam Strategy & Shortcut Use the unit digit or approximation to verify your answer quickly. The sum is roughly 122 and the difference is roughly 35. $122 \times 35$ is approximately $4270$. Looking at the exact decimals, $0.6 \times 0.3$ will end in an $8$. Option (d) $4353.88$ matches both the approximate magnitude and the final decimal digit perfectly. ### Common Pitfall Squaring $78.95$ and $43.35$ independently. This is computationally heavy and highly error-prone under time pressure. Always look for algebraic identities first. ### Final Answer Therefore, the correct answer is 4353.88.