Question
Solve:
$a^2+2 a-3$
$a^2+2 a-3$
✓
Answer
$a^2+2 a-3$
$= a ^2+2 a +\left(\frac{2}{2}\right)^2-\left(\frac{2}{2}\right)^2-3\left[\right.$ Adding and subtracting $\left(\frac{2}{2}\right)^2$, that is $\left.1^2\right]$
$=a 2+2 a+1-1-3$
$=(a+1) 2-4[$ Comleting the square]
$=(a+1) 2-22$
$=[(a+1)-2][(a+1)+2]$
$=(a+1-2)(a+1+2)$
$=(a-1)(a+3)$
$= a ^2+2 a +\left(\frac{2}{2}\right)^2-\left(\frac{2}{2}\right)^2-3\left[\right.$ Adding and subtracting $\left(\frac{2}{2}\right)^2$, that is $\left.1^2\right]$
$=a 2+2 a+1-1-3$
$=(a+1) 2-4[$ Comleting the square]
$=(a+1) 2-22$
$=[(a+1)-2][(a+1)+2]$
$=(a+1-2)(a+1+2)$
$=(a-1)(a+3)$
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