Question

evaluate x^8-y^8 using identity​

Answer 1

Answer:

(x^4+y^4)(x^4-y^4)

Step-by-step explanation:

use identity a^2-b^2=(a+b)(a-b)

Answer 2

$\underline { \blue { By \: Algebraic\: Identity :}}$

$\boxed { \pink { a^{2} - b^{2} = ( a + b )( a - b ) }}$

$Here ,\red{ x^{8} - y^{8}} \\= (x^{4})^{2} - (y^{4})^{2} \\= (x^{4} + y^{4} ) (x^{4} - y^{4} ) \\= (x^{4} + y^{4} ) [(x^{2})^{2} - (y^{2} )^{2}] \\= (x^{4} + y^{4} ) (x^{2} + y^{2} )( x^{2} - y^{2} ) \\= (x^{4} + y^{4} ) (x^{2} + y^{2} )( x + y )( x - y )$

Therefore.,

$\red{Factors \:of \: x^{8} - y^{8}}$

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

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