Question
Multiply:
$ \left(x^6-y^6\right) \text { by }\left(x^2+y^2\right) $
$ \left(x^6-y^6\right) \text { by }\left(x^2+y^2\right) $
✓
Answer
To multiply, we will use distributive law as follows:
$ \left(x^6-y^6\right) \text { by }\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 $.
$ \left(x^6-y^6\right) \text { by }\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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Pattern
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$1$
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$2$
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$3$
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$5$
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$6$
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