factorise x^8 + y^8 as real quadratic factor.
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(x⁴)² + (y⁴)²
=( x⁴ + y⁴)² -2x⁴y⁴
={ (x²)² + (y²)² }² -2x⁴y ⁴
={(x² + y²)² -2x²y²}² -2x⁴y⁴
=[ {(x² +y² -√2xy)(x² +y²+√2xy)} -√2x²y²}{(x² +y² -√2xy)(x² +y²+√2xy)+√2x²y² }]
=( x⁴ + y⁴)² -2x⁴y⁴
={ (x²)² + (y²)² }² -2x⁴y ⁴
={(x² + y²)² -2x²y²}² -2x⁴y⁴
=[ {(x² +y² -√2xy)(x² +y²+√2xy)} -√2x²y²}{(x² +y² -√2xy)(x² +y²+√2xy)+√2x²y² }]
Murugan11:
i am suffering this question from a long time so thank you.
thanks dear very nice of you
ok
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