Question

factorise 25÷4 x^2-y^2÷9

Answer 1

25/4x^2 -y^2/9

(5/2x)^2 -(y/3)^2

(5/2x-y/3)(5/2x+y/3)

Answer 2

Answer:

$\text{The factored form is }(\frac{5}{2}x-\frac{y}{3})(\frac{5}{2}x+\frac{y}{3})$

Step-by-step explanation:

Given the expression

$\frac{25}{4}x^2-\frac{y^2}{9}$

we have to factorise the above polynomial.

$\frac{25}{4}x^2-\frac{y^2}{9}$

$(\frac{5}{2}x)^2-(\frac{y}{3})^2$

Using identity

$a^2-b^2=(a-b)(a+b)$

$Put\thinspace a=\frac{5}{2}x\text{ and }b=\frac{y}{3}$

$(\frac{5}{2}x)^2-(\frac{y}{3})^2=(\frac{5}{2}x-\frac{y}{3})(\frac{5}{2}x+\frac{y}{3})$

which is required factored form.