Question

please answer these two questions
(Polynomials)​

Answer 1

Step-by-step explanation:

${a}^{4} - a = a( {a}^{3} - 1) \\ \\ = a(a - 1)( {a}^{2} + a + 1).$

${x}^{8} - {y}^{8} = { ({x}^{4}) }^{2} - { ({y}^{4}) }^{2} \\ \\ =( {x}^{4} + {y}^{4} )( {x}^{4} - {y}^{4} ) \\ \\ = ( {x}^{4} + {y}^{4} )( {x}^{2} - {y}^{2} )( {x}^{2} + {y}^{2} ) \\ \\ = ( {x}^{4} + {y}^{4} )(x + y)(x - y)( {x}^{2} + {y}^{2} ).$