Question

Simplify : (x − y)(x + y) (x² + y²)(x⁴ + y²)

Answer 1

To simplify, we will proceed as follows:

\[ \left( x - y \right)\left( x + y \right)\left( x^2 + y^2 \right)\left( x^4 + y^4 \right)\]

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

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

\[ = x^8 - x^8 \left[ \because \left( a + b \right)\left( a - b \right) = a^2 - b^2 \right]\]