Question

$\text{Factorise:}{x}^2+6x+9-x-3$

• A. $(x-2)(x+3)$
• B. $(x+2)(x+3)$
• C. $(x+2)(x-3)$
• D. $(x-2)(x-3)$

Answer 1

The correct option is B

$(x+2)(x+3)$

$\text{We need to factorise the given}\text{expression:}$
$x^2+6x+9-x-3$

$\text{Consider the first three terms of the}\text{given expression:}{x}^2+6x+9.$

$\text{On comparing}{x}^2+6x+9\text{with the}\text{identity}(a+b{)}^2=a^2+2ab+b^2,\text{we get,}{x}^2+6x+9=(x+3{)}^2.$

$\text{Hence,}{x}^2+6x+9-x-3=(x+3{)}^2-x-3=(x+3\left)\right(x+3)-1(x+3)$

$\text{Taking (x+3) common , we get}$

$(x+3)\left(\right(x+3)-1)=(x+3)(x+2)$

$\text{Thus,}{x}^2+6x+9-x-3=(x+3)(x+2)$