factorise x^412y^4-y^412x^4
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Step-by-step explanation:
ANSWER
Here again we add and subtract suitable terms to bring it in a factorisation form. Notice that
x
4
+4y
4
=(x
2
)
2
+(2y
2
)
2
−2(x
2
)(2y
2
)−(2xy)
2
=(x
2
+2y
2
)
2
−(2xy)
2
The second expression is in the form a
2
−b
2
, where a=(x
2
+2y
2
) and b=2xy
Hence we may write
x
4
+4y
4
=(x
2
+2y
2
+2xy)(x
2
+2y
2
−2xy)
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