Question

factorise the following 1 + x square + 9 y square + 2 x minus 6 x y minus 6y

Answer 1

$1 + {x}^{2} + 9 {y}^{2} + 2x - 6xy - 6y \\ = {x}^{2} - 6xy + 9 {y}^{2} + 2x - 6y + 1 \\ = ({x}^{2} - 6xy + 9 {y}^{2} ) + 2(x - 3y) + 1 \\ = ( {x - 3y})^{2} + 2(x - 3y) + 1 \\ = ( {x - 3y + 1})^{2}$