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Given the expression: $$1234567893 \times 1234567894 - 1234567895 \times1234567892$$ Is it correct to say that the answer is $ (3 \times 4) - (5 \times 2) $? If so, why?

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up vote 16 down vote accepted

HINT : $$(x+3)(x+4)-(x+5)(x+2)=3\times 4-5\times 2$$

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Brilliant! $\;$ – David Simmons Aug 19 '14 at 16:00
@Chadman: Thank you!:) – mathlove Aug 19 '14 at 16:01

Hint $\ a\!+\!b = c\!+\!d\,\Rightarrow\, (x\!+\!a)(x\!+\!b)-(x\!+\!c)(x\!+\!d) = ab\!-\!cd,\ $ and conversely.

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Hint: Let $a=123456789$. Then your problem can be written as $(10a+3)(10a+4)-(10a+5)(10a+2)$

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let x=1234567890 (x+3)(x+4)-(x+2)(x+5) As x terms get cancelled due to the sum of their last digits being equal,therefore answer can be obtained directly from their last digits. (3*4)-(5*2)=2

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