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Question
If x = 3 and y = − 1, find the values of the following using in identify:
(9y2 − 4x2) (81y4 +36x2y2 + 16x4)
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Solution
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`.
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