Question

Factorise the expression into factors by expressing them as the difference of two squares: $x^2–2x–3$ (2 Marks)

Answer 1

$x^2-2x-3$
$=x^2-2\times x\times 1+(1{)}^2-(1{)}^2-3$
$=(x-1{)}^2-4$ (1 Mark)
$=(x-1{)}^2-2^2$
$=(x-1-2)(x-1+2)[since,a^2-b^2=(a-b\left)\right(a+b\left)\right]$
$=(x-3)(x+1)$ (1 Mark)