Question

$(x ^{2} + y ^{2} )(x ^{2} + y ^{2} )$

Answer 1

$\textbf{\huge{ANSWER:}}$

Identity:

${(x + y)}^{2} = {x}^{2} + {y}^{2} + 2xy$


ATQ:

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

Answer 2

Hey!!

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


ANOTHER ALTERNATIVE METHOD :-

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

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Hope it Helps!!