factorise: 81x^⁴-y^⁴
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Answer:
Given : 81x
4
−y
4
We can further write it as
81x
4
−y
4
=(9x
2
)
2
−(y
2
)
2
Based on the equation a
2
−b
2
=(a+b)(a−b)
We get,
81x
4
−y
4
=(9x
2
+y
2
)(9x
2
−y
2
)
On further simplification using the formula
81x
4
−y
4
=(9x
2
+y
2
)((3x
2
)
2
−y
2
)
So we get,
81x
4
−y
4
=(9x
2
+y
2
)(3x+y)(3x−y)
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