Question

factorise: 81x^⁴-y^⁴
​

Answer 1

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)