Question

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1). Find the product of :
i). (a2+b2) (a4+b4) (a+b) (a-b)
ii). (2x-y+3) (2x-y-3)

Answer 1

1st answer is
(a^2+b^2) (a^4+b^4) (a+b) (a-b)
(a^2+b^2) (a^4+b^4) (a^2-b^2)
(a^4+b^4) (a^4-b^4)
(a^8-b^8)

2nd answer
a=(2x-y) b=3
(a+b) (a-b)=(a^2-b^2)

(2x-y)^2-(3)^2
4x^2+y^2-4xy-9

Answer 2

$\textbf{Answer is as follows :}$

1) Let's assume a to be x and b to be y.



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




Now, we will use identity (a+b)(a-b)=a^2 - b^2


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


Now again the same identity will be used.


$( {x}^{4} + {y}^{4} )( {x}^{4} - {y}^{4} )$


Now again the same identity will be used.


${ ({x}^{4})}^{2} - {( {y}^{4}) }^{2}$


This is equal to:-


${x}^{8} - {y}^{8}$


Substituting the values of x and y , we get


${a}^{8} - {b}^{8}$. ( Ans )


ii)


$(2x - y + 3)(2x - y - 3)$


This can also be written as :-


$((2x - y) + (3))((2x - y) - (3))$


Now this is in the form of ( a+b) (a-b) .Here a = 2x - y and b = 3


According to this identity , (a+b)(a-b)=a^2-b^2


Using this identity ,


${(2x - y)}^{2} - {(3)}^{2}$


We will expand it using the identity ( a-b)^2 = a^2 + b^2 - 2 ab . Here a = 2x and b = y


Now, expanding it we get :


$4 {x}^{2} + {y}^{2} + 4xy - 9$. ( Ans )