Question

(x-y)(x+y)(x² +y² )(x⁴+y⁴) is equal to
A. x¹⁶ – y¹⁶
B. x⁸ –y⁸
C. x⁸+y⁸
D. x¹⁶ + y¹⁶

Answer 1

Answer:

(x+y)(x-y)(x^2+y^2)(x^4+y^4)

= (x^2-y^2)(x^2+y^2)(x^4+y^4)

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

= x^8-y^8

Hope this helps you !

Answer 2

Given : (x  - y)(x + y)(x² + y² )(x⁴ + y⁴)  

Solution :

We have :  (x - y)(x + y)(x² + y² )(x⁴ + y⁴)

By using the identity:  (a - b ) (a + b ) = a² - b²

=  ( x² - y² ) ( x² + y² ) ( x⁴ + y⁴ )

=  ( (x²)² - (y²)² ) ( x⁴ + y⁴ )

=  ( x⁴ - y⁴ ) ( x⁴ + y⁴ )

=  (x⁴)² - (y⁴)²

(x - y)(x + y)(x² + y² )(x⁴ + y⁴) = x⁸ - y⁸

Hence , (x  - y)(x + y)(x² + y² )(x⁴ + y⁴) is equal to x⁸ - y⁸

Among the given options option (B) x⁸ – y⁸ is correct .  

HOPE THIS ANSWER WILL HELP YOU……

 

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