Question

factorise 81x square/4-y square/49​

Answer 1

Given:

$\frac{81x^{2} }{4}$-$\frac{y^{2} }{49}$

To find:

A factor of the above expression

Solution:

$\frac{81x^{2} }{4}$-$\frac{y^{2} }{49}$

make a perfect square

($\frac{9x}{2}$)²-($\frac{y}{7}$)²

use algebraic identity

a²-b²=(a+b)(a-b)

=($\frac{9x}{2}$+$\frac{y}{7}$)($\frac{9x}{2}$-$\frac{y}{7}$)

Hence, $\frac{81x^{2} }{4}$-$\frac{y^{2} }{49}$ = ($\frac{9x}{2}$+$\frac{y}{7}$)($\frac{9x}{2}$-$\frac{y}{7}$)