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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asked Aug 19, 2014 at 15:53
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4 Answers
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HINT : $$(x+3)(x+4)-(x+5)(x+2)=3\times 4-5\times 2$$
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Hint $\ a\!+\!b = c\!+\!d\,\Rightarrow\, (x\!+\!a)(x\!+\!b)-(x\!+\!c)(x\!+\!d) = ab\!-\!cd,\ $ and conversely.
answered Aug 19, 2014 at 16:04
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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 $x=1234567890$, then $(x+3)(x+4)-(x+2)(x+5)$. 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.
Therefore.... $$(3*4)-(5*2)=2$$
