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Difference of Squares Simplification

Source: 2020 AMC 12B #2

February 6, 2020
AMCAMC 122020 AMC 12Balgebradifference of squaresspecial factorizations2020 AMC

Problem Statement

What is the value of the following expression? 1002−72702−112⋅(70−11)(70+11)(100−7)(100+7)\frac{100^2-7^2}{70^2-11^2} \cdot \frac{(70-11)(70+11)}{(100-7)(100+7)} <spanclass=′latex−bold′>(A)</span>1<spanclass=′latex−bold′>(B)</span>99519950<spanclass=′latex−bold′>(C)</span>47804779<spanclass=′latex−bold′>(D)</span>108107<spanclass=′latex−bold′>(E)</span>8180<span class='latex-bold'>(A) </span> 1 \qquad <span class='latex-bold'>(B) </span> \frac{9951}{9950} \qquad <span class='latex-bold'>(C) </span> \frac{4780}{4779} \qquad <span class='latex-bold'>(D) </span> \frac{108}{107} \qquad <span class='latex-bold'>(E) </span> \frac{81}{80}
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