Question

Factorise : $x^2+6x+9-4y^2$

Answer 1

$x^2+6x+9-4y^2=(x{)}^2+2\times x\times 3+(3{)}^2-(2y{)}^2\left\{\begin{array}{c}\because (a+b{)}^2=a^2+2ab+b^2\\ a^2-b^2=(a+b)(a-b)\end{array}\right\}=(x+3{)}^2-(2y{)}^2=(x+3+2y\left)\right(x+3-2y)=(x+2y+3\left)\right(x-2y+3)$