Question

If x = −2 and y = 1, by using an identity find the value of the following

 4y^{2 −} 9x² (16y⁴ + 36x²y²+81x⁴)

Answer 1

n the given problem, we have to find the value of   (4y^{2 −} 9x²) (16y⁴ + 36x²y²+81x⁴) using identity

Given  x=-2 y  = 1

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

We can rearrange the  4y^{2 −} 9x² (16y⁴ + 36x²y²+81x⁴) as

`(4y^2 - 9x^2 ) (16y^4 + 36x^2 + 81x^4) = (4y^2 - 9x^2)((4y^2)^2 + 4y^2 xx 9x^2 + (9x^2)^2)`

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

\[= \left( 4 y^2 \right) \times \left( 4 y^2 \right) \times \left( 4 y^2 \right) - \left( 9 x^2 \right) \times \left( 9 x^2 \right) \times \left( 9 x^2 \right)\]
\[ = 64 y^6 - 729 x^6\]

Now substituting the value   x = -2 , y =1 in  `64y^6 - 729x^6`we get,

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

` = 64(1)^6 - 729(-2)^6`

` = 64 - 729(64)`

Taking 64 as common factor in above equation we get,

` = 64 (1-729)`

` = 64 xx -728`

` = -46592`

Hence the Product value of  (4y^{2 −} 9x² )(16y⁴ + 36x²y²+81x⁴)  is ` = -46592`.