Question

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

(i) 4y^{2 −} 9x² (16y⁴ + 36x²y²+81x⁴)

(ii) $\left(\frac{2}{x}-\frac{x}{2}\right)\left(\frac{4}{x^2}+\frac{x^2}{4}+1\right)$

(iii) $\left(5y+\frac{15}{y}\right)\left(25y^2-75+\frac{225}{y^2}\right)$

Answer 1

(i) In the given problem, we have to find the value of using identity

Given

We shall use the identity

We can rearrange the as

$$\begin{gathered} =\left(4y^2\right)\times \left(4y^2\right)\times \left(4y^2\right)-\left(9x^2\right)\times \left(9x^2\right)\times \left(9x^2\right) \\ =64y^6-729x^6 \end{gathered}$$
Now substituting the value in we get,

Taking 64 as common factor in above equation we get,

Hence the Product value of is

(ii) In the given problem, we have to find the value of using identity

Given

We shall use the identity

We can rearrange the as

$$\begin{gathered} =\left(\frac{2}{x}\right)\times \left(\frac{2}{x}\right)\times \left(\frac{2}{x}\right)-\left(\frac{x}{2}\right)\times \left(\frac{x}{2}\right)\times \left(\frac{x}{2}\right) \\ =\frac{8}{x^3}-\frac{x^3}{8} \end{gathered}$$

Now substituting the value in we get,

Hence the Product value of is = 0.

(iii) Given

We shall use the identity,

We can rearrange the as

Now substituting the value in

Hence the Product value of is