Question

factorise 9 X square + 6 X + 1 minus 25 y square

Answer 1

$9 {x}^{2} + 6x + 1 - 25 {y}^{2} \\ = {(3x + 1)}^{2} - {(5y)}^{2} \\ = (3x + 5y + 1)(3x - 5y + 1)$
Formulae used:
${x}^{2} + 2xy + {y}^{2} = {(x + y)}^{2}$
${x}^{2} - {y}^{2} = (x + y)(x - y)$