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$x^{16} + y^{16}$
$(x-y)(x+y)=x^2-y^2\left[\text { by identity }(a+b)(a-b)=a^2-b^2\right]$
$\left(x^2-y^2\right)\left(x^2+y^2\right)=x^4-y^4$
$\left(x^4-y^4\right)\left(x^4+y^4\right)=x^8-y^8$
$\text { Now, }$
$(x-y)(x+y)\left(x^2+y^2\right)\left(x^4+y^4\right)$
$=\left(x^2-y^2\right)\left(x^2+y^2\right)\left(x^4+y^4\right)$
$=\left(x^4-y^4\right)\left(x^4+y^4\right)$
$=x^8-y^8$
Hence, correct option is $(b).$
Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.