Question

Factorize the following using the appropriate identities:-
$4{x^2} - \dfrac{{{y^2}}}{{25}}$.

Answer 1

Hint – In order to solve the problem you have to use the formula ${a^2} - {b^2} = (a - b)(a + b)$. You just need to have an idea of squares from 1-10.

Complete step-by-step answer:
The given equation is $4{x^2} - \dfrac{{{y^2}}}{{25}}$.

We will factorize this equation using the formula ${a^2} - {b^2} = (a - b)(a + b)$……..(1)

We know that $4{x^2}$ can be written as ${(2x)^2}$ and $\dfrac{{{y^2}}}{{25}}$ can be written as ${\left( {\dfrac{y}{5}} \right)^2}$.

On substituting these values in the given equation we get the equation as:-
$4{x^2} - \dfrac{{{y^2}}}{{25}} = {(2x)^2} - {\left( {\dfrac{y}{5}} \right)^2} = \left( {2x - \dfrac{y}{5}} \right)\left( {2x + \dfrac{y}{5}} \right)$ (From (1))

Hence the answer to this question is $\left( {2x - \dfrac{y}{5}} \right)\left( {2x + \dfrac{y}{5}} \right)$.

Note – The tricky part in this question is that we know the square of 2 is 4 and that of 5 is 25 using this we factorize the equation by using the identities that give the right answer.