Question

factorise the following​

Answer 1

Answer:

There are three terms– two squares of "x" and "y" and one "xy".

The thing that most associates itself with such terms is the expansion of (a + b)².

For this, try to covert the square terms to proper squares and get a 2 multiplied by each term in the middle. This helps you convert this into the (a + b)² format.

$\mathsf{ \frac{ {x}^{2} }{9} + 6xy + 81 {y}^{2} }$

$\implies \mathsf{ \frac{ {x}^{2} }{ {3}^{2} } + 2 \times 3xy + {(9y)}^{2} }$

$\implies \mathsf{( {\frac{ {x} }{ {3} })} {}^{2} + 2 \times 9 \times \frac{1}{3} xy + {(9y)}^{2} }$

(a + b)² = a² + 2ab + b²

$\implies \mathsf{( \frac{x}{3} + 9y) {}^{2} }$