Question

If x = 3 and y = − 1, find the values of the following using in identify:

 (9y² − 4x²) (81y⁴ +36x²y² + 16x⁴)

Answer 1

In the given problem, we have to find the value of equation using identity

(i) Given  (9y² − 4x²) (81y⁴ +36x²y² + 16x⁴)

We shall use the identity  `(a- b) (a^2 + ab + b^2) = (a^3 - b^3)`

We can rearrange the  (9y² − 4x²) (81y⁴ +36x²y² + 16x⁴)as

`(9y^2 - 4x^2) ((9y^2)^2) + 9y^2 xx 4x^2 + (4x^2)^2)`

`= (9y^2)^3 - (4x^2)^3`

` = (9y^2) xx (9y^2) xx (9y^2) + (4x^2) xx (4x^2) xx(4x^2)  `

`= 729y^6 - 64x^6`

Now substituting the value  x =,y = -1 in `729y^6 - 64x^6`we get,

`729y^6 - 64x^6`

`729(-1)^6 - 64(3)^6`

`729(1) - 64(729)`

`729 - 46656`

`=-45927`

Hence the Product value of (9y² − 4x²) (81y⁴ +36x²y² + 16x⁴)is  `=-45927`.