Question

$(x-y)(x+y)(x^2+y^2)(x^4+y^4)\text{is equal to}$

• A. $x^{16}-y^{16}$
• B. $x^8-y^8$
• C. $x^8+y^8$
• D. $x^{16}+y^{16}$

Answer 1

The correct option is B

$x^8-y^8$

$(x-y)(x+y)(x^2+y^2)(x^4+y^4)=(x^2-y^2)(x^2+y^2)(x^4+y^4)\{\because (a+b\left)\right(a-b)=a^2-b^2\}=\left[\right(x^2{)}^2-\left(y^2{)}^2\right](x^4+y^4)=(x^4-y^4)(x^4+y^4)=(x^4{)}^2-(y^4{)}^2=x^8-y^8$