Question

Factorise: $(25÷4)x^2-y^2÷9$

Answer 1

Factorization:

The given equation is,

$(25÷4)x^2-y^2÷9=\frac{25}{4}{x}^2-\frac{y^2}{9}$

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

We know that,

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

$\therefore (25÷4)x^2-y^2÷9=\left(\frac{5x}{2}+\frac{y}{3}\right)\left(\frac{5x}{2}-\frac{y}{3}\right)$

Hence, the result of factorization of the given equation is $\left(\frac{5x}{2}+\frac{y}{3}\right)\left(\frac{5x}{2}-\frac{y}{3}\right)$.