Question

simplify- (a2+b2)(a2+a2)-(a2-b2)(a2-b2)​

Answer 1

Answer:

4 a^2 b^2

Step-by-step explanation:

( a^2 + b^2 ) ( a^2 + b^2 ) - ( a^2 - b^2 ) ( a^2 - b^2 ) = ?

( a^2 + b^2 ) ( a^2 + b^2 )

= a^2 ( a^2 + b^2 ) + b^2 ( a^2 + b^2 )

= a^4 + a^2 b^2 + a^2 b^2 + b^4

= a^4 + 2 a^2 b^2 + b^4

( a^2 - b^2 ) ( a^2 - b^2 )

= a^2 ( a^2 - b^2 ) - b^2 ( a^2 - b^2 )

= a^4 - a^2 b^2 - a^2 b^2 + b^4

= a^4 - 2 a^2 b^2 + b^4

( a^2 + b^2 ) ( a^2 + b^2 ) - ( a^2 - b^2 ) ( a^2 - b^2 )

= a^4 + 2 a^2 b^2 + b^4 - ( a^4 - 2 a^2 b^2 + b^4 )

= a^4 + 2 a^2 b^2 + b^4 - a^4 + 2 a^2 b^2 - b^4

= a^4 - a^4 + b^4 - b^4 + 2 a^2 b^2 + 2 a^2 b^2

= 0 + 0 + 4 a^2 b^2

=  4 a^2 b^2

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