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Question
Multiply:
(x6 − y6) by (x2 + y2)
Solution
To multiply, we will use distributive law as follows:
\[\left( x^6 - y^6 \right)\left( x^2 + y^2 \right)\]
\[ = x^6 \left( x^2 + y^2 \right) - y^6 \left( x^2 + y^2 \right)\]
\[ = \left( x^8 + x^6 y^2 \right) - \left( y^6 x^2 + y^8 \right)\]
\[ = x^8 + x^6 y^2 - y^6 x^2 - y^8\]
Thus, the answer is \[x^8 + x^6 y^2 - y^6 x^2 - y^8\].
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