document.write( "Question 282933: The binomial x²-81 is called a _________ of two__________, and will factor in to(______)(_______)? \n" ); document.write( "

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The binomial x²-81 is called a _________ of two__________, and will factor in to(______)(_______)?\r
\n" ); document.write( "\n" ); document.write( " $\"x%5E2-81\"$ is called a difference of two squares. The formula is $\"a%5E2-b%5E2=%28a%2Bb%29%28a-b%29\"$ . You can check by foiling (a+b)(a-b). When you foil (a+b)(a-b) you get $\"a%5E2-ab%2Bab-b%5E2\"$ the -ab and the +ab cancel out. Leaving you $\"a%5E2-b%5E2\"$ . \r
\n" ); document.write( "\n" ); document.write( "In the binomial $\"x%5E2-81\"$ , $\"x%5E2\"$ is a perfect square and so is 81. The square root of $\"x%5E2\"$ is x and the square root of 81 is 9. $\"x%5E2-81\"$ = $\"x%5E2-9%5E2\"$ , that factors to (x+9)(x-9). So to check you can foil (x+9)(x-9) you get $\"x%5E2-9x%2B9x-81\"$ , the -9x and the +9x cancel and you have your original binomial. $\"x%5E2-81\"$ .\r
\n" ); document.write( "\n" ); document.write( "The answer is: The binomial $\"x%5E2-81\"$ is called a difference of two squares, and will factor in to (x+9)(x-9). \n" ); document.write( "

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