Question

1) x^4-81y^4
2) 2x^5-2x

Answer 1

1)=(x^2+9y^2)(x^2-9y^2)
=(x^2+9y^2)(x-3y)(x+3y)
(using a2 -b2 =(a-b) (a+b)
2)2x(2x^4-1)
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Answer 2

Hello...
Answer...

1)

${x}^{2} - {81y}^{2} \\ \\ = {(x}^{2} ) {}^{2} - ( {9y}^{2} {)}^{2} \\ \\ = ( {x}^{2} - {9y}^{2} )( {x}^{2} + {9y}^{2} ) \\ \\ = { {x}^{2} - ( {3y}^{2} )}( {x}^{2} + {9y}^{2} ) \\ \\ = (x - 3y)( x + 3y)( {x}^{2} + {9y}^{2} )$


2)

${2x}^{5} - 2x = 2x( {x}^{4} - 1) \\ \\ = 2x( {x}^{2} ) {}^{2} - {1}^{2}) \\ \\ = 2x( {x}^{2} - 1)( {x}^{2} + 1) \\ \\ = 2x(x - 1)(x + 1)( {x}^{2} + 1)$


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