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Check whether the following are quadratic equations:
$(x – 2) (x + 1) = (x – 1) (x + 3)$
Given:
Given equation is $(x – 2) (x + 1) = (x – 1) (x + 3)$
To do:
We have to check whether the given equation is quadratic.
Solution:
The standard form of a quadratic equation is $ax^2+bx+c=0$.
$(x – 2) (x + 1) = (x – 1) (x + 3)$
$x(x+1)-2(x+1)=x(x+3)-1(x+3)$
$x^2+x-2x-2=x^2+3x-x-3$
$x^2-x^2-x-2x-2+3=0$
$-3x+1=0$ is not of the form $ax^2+bx+c=0$
Therefore, $(x – 2) (x + 1) = (x – 1) (x + 3)$  is not a quadratic equation. 
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