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Question
Simplify : (x − y)(x + y) (x2 + y2)(x4 + y2)
Solution
To simplify, we will proceed as follows:
\[ \left( x - y \right)\left( x + y \right)\left( x^2 + y^2 \right)\left( x^4 + y^4 \right)\]
\[ = \left( x^2 - y^2 \right)\left( x^2 + y^2 \right)\left( x^4 + y^4 \right) \left[ \because\left( a + b \right)\left( a - b \right) = a^2 - b^2 \right]\]
\[ = \left( x^4 - y^4 \right)\left( x^4 + y^4 \right) \left[ \because \left( a + b \right)\left( a - b \right) = a^2 - b^2 \right]\]
\[ = x^8 - x^8 \left[ \because \left( a + b \right)\left( a - b \right) = a^2 - b^2 \right]\]
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