document.write( "Question 207728: What is the counter example of \"The product of a number (n-1) and number (n+1) is always equal to n^2-1?\" \n" ); document.write( "

Algebra.Com's Answer #157116 by jim_thompson5910(35256) $\"\"$ $\"About$

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If you FOIL out $\"%28n-1%29%28n%2B1%29\"$ , you will get: $\"%28n-1%29%28n%2B1%29=n%2An%2Bn%2A1-1%2An-1%2A1=n%5E2%2Bn-n-1=n%5E2-1\"$ \r
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\n" ); document.write( "\n" ); document.write( "So $\"%28n-1%29%28n%2B1%29=n%5E2-1\"$ is true for ALL values of 'n'\r
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\n" ); document.write( "\n" ); document.write( "This means that \"The product of a number (n-1) and number (n+1) is always equal to n^2-1\" is ALWAYS true. So once again, we cannot find any counter examples because there are none in this case.\r
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