Question

factorise:-
$\frac{x ^{2} }4 + \frac{3xy}{4} + \frac{9y {}^{2} }{16}$

Answer 1

$\frac{ {x}^{2} }{4} + \frac{3xy}{4} + \frac{ {9y}^{2} }{16}\\ \\ = \frac{ {4x}^{2} + 12xy + {9y}^{2} }{16}\\ \\ = \frac{ {4x}^{2} + (9 + 4)xy + {9y}^{2} }{16} \\ \\ = \frac{ {4x}^{2} + 9xy + 4xy + {9y}^{2} }{16} \\ \\ = \frac{x(4x + 9y) + y(4x + 9y)}{16}\\ \\ = \frac{(x + y)(4x + 9y)}{16}$