MCQ
$(x - y) (x + y) (x^2 + y^2) (x^4+ y^4)$ is equal to:
  • A
    $x^{16} - y^{16}$
  • $x^8 - y^8$
  • C
    $x^8 + y^8$
  • D
    $x^{16} + y^{16}$

Answer

Correct option: B.
$x^8 - y^8$

 $(x-y)(x+y)=x^2-y^2\left[\text { by identity }(a+b)(a-b)=a^2-b^2\right]$
$\left(x^2-y^2\right)\left(x^2+y^2\right)=x^4-y^4$
$\left(x^4-y^4\right)\left(x^4+y^4\right)=x^8-y^8$
$\text { Now, }$
$(x-y)(x+y)\left(x^2+y^2\right)\left(x^4+y^4\right)$
$=\left(x^2-y^2\right)\left(x^2+y^2\right)\left(x^4+y^4\right)$
$=\left(x^4-y^4\right)\left(x^4+y^4\right)$
$=x^8-y^8$
Hence, correct option is $(b).$

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