Question

Find the value of (5/2x+y/3)(5/2x-y/3)​

Answer 1

$\tt{ (\dfrac{5}{2}x + \dfrac{y}{3}) (\dfrac{5}{2}x - \dfrac{y}{3})}$

If we carefully observe the given problem ; we can understand that it is in the form of the identity (a + b) (a - b).

So we will use the same identity to solve the given problem.

Here a => $\tt{ \dfrac{5}{2}x}$

b => $\tt{ \dfrac{y}{3}}$

We know the expansion of the identity :

$\large{\boxed{\tt{(a+b)(a-b) \implies {(a)}^{2} - {(b)}^{2}}}}$

After putting up the values of (a) and (b) we get :

$\tt{ (\dfrac{5}{2}x + \dfrac{y}{3})(\dfrac{5}{2}x - \dfrac{y}{3}) \implies {(\dfrac{5}{2}x}^{2}) - {(\dfrac{y}{3}}^{2})}$

$\boxed{\tt{(\dfrac{5}{2}x + \dfrac{y}{3})(\dfrac{5}{2}x - \dfrac{y}{3}) \implies {\dfrac{25}{4}x - \dfrac{{y}^{2}}{9}}}}$

Answer :

$\large{\boxed{\tt{ \dfrac{25}{4}x - \dfrac{{y}^{2}}{9}}}}$

There are many such identities. Some of them are :

• $\tt{ {(a+b)}^{2} \implies {a}^{2} + {b}^{2} + 2ab}$

• $\tt{ {(a-b)}^{2} \implies {a}^{2} + {b}^{2} -2ab}$

• $\tt{ (a+b)(a-b) \implies {a}^{2} - {b}^{2}}$

• $\tt{(x+a)(x+b) \implies {x}^{2} + (a+b)x + ab}$