document.write( "Question 357583: How do you factor completely x^8-y^20? \n" ); document.write( "

Algebra.Com's Answer #255297 by nerdybill(7384) $\"\"$ $\"About$

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Think \"difference of squares\"...
\n" ); document.write( "A^2-B^2 = (A-B)(A+B)
\n" ); document.write( "And, \"sum of squares\"...
\n" ); document.write( "A² + B² = (A + B + √(2AB)) (A + B − √(2AB))
\n" ); document.write( ".
\n" ); document.write( "x^8-y^20
\n" ); document.write( "Can be rewritten as:
\n" ); document.write( "(x^4)^2 - (y^10)^2
\n" ); document.write( "which can be factored as
\n" ); document.write( "(x^4-y^10)(x^4+y^10)
\n" ); document.write( ".
\n" ); document.write( "rewriting the above:
\n" ); document.write( "((x^2)^2-(y^5)^2)((x^2)^2+(y^5)^2)
\n" ); document.write( "(x^2-y^5)(x^2+y^5)(x^2+y^5+√(2x^2y^5))(x^2+y^5-√(2x^2y^5))
\n" ); document.write( "(x^2-y^5)(x^2+y^5)(x^2+y^5+xy^2√(2y))(x^2+y^5-xy^2√(2y)) \n" ); document.write( "

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