document.write( "Question 44989: Factor the polynomial completely\r
\n" ); document.write( "\n" ); document.write( " $\"x%5E2-y%5E2%2B18y-81\"$ \n" ); document.write( "

Algebra.Com's Answer #29893 by Earlsdon(6294) $\"\"$ $\"About$

You can put this solution on YOUR website!
You can factor this expression in steps:\r
\n" ); document.write( "\n" ); document.write( " $\"x%5E2-y%5E2%2B18y-81\"$ Group the last three terms.
\n" ); document.write( " $\"x%5E2-%28y%5E2-18y%2B81%29\"$ Note the change of signs due to the introduction of the parentheses. You can verify that this is the same as the original expression using the distributive property.\r
\n" ); document.write( "\n" ); document.write( "Now factor the trinomial in the parentheses.\r
\n" ); document.write( "\n" ); document.write( " $\"%28y%5E2-18y%2B81%29+=+%28y-9%29%28y-9%29\"$ = $\"%28y-9%29%5E2\"$ So now you have:\r
\n" ); document.write( "\n" ); document.write( " $\"x%5E2-%28y-9%29%5E2\"$ Which, as you can see, is the difference of two squares, and which factors nicely. To wit! $\"A%5E2-B%5E2+=+%28A%2BB%29%28A-B%29\"$ , so...\r
\n" ); document.write( "\n" ); document.write( " $\"x%5E2-%28y-9%29%5E2+=+%28x%2B%28y-9%29%29%28x-%28y-9%29%29\"$ Simplifying, you get:\r
\n" ); document.write( "\n" ); document.write( " $\"%28x%2By-9%29%28x-y%2B9%29\"$ as the factors of the expression $\"x%5E2-y%5E2%2B18y-81\"$ \n" ); document.write( "

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