Check whether the following is quadratic equation :

$(x-2)(x+1)=(x-1)(x+3)$

Check whether the following is quadratic equation:

$(x-3)(2 x+1)=x(x+5)$

Check whether the following are quadratic equations :

$(2 x-1)(x-3)=(x+5)(x-1)$

Check whether the following are quadratic equations :

$x^2+3x+1=(x-2{)}^2$

Check whether the following is a quadratic equation:

$(x + 2{)}^3=2x(x^2–1)$

Check whether the following is a quadratic equation:

$x^3-4x^2-x+1=(x-2{)}^3$

Represent the following situation in the form of quadratic equation:

The area of a rectangular plot is $528 {\mathrm{m}}^2$. The length of the plot is one metre more than twice its breadth. We need to find the length and breadth of the plot.

Represent the following situation in the form of quadratic equation:

The product of two consecutive positive integers is $306.$ We need to find the integers.

Represent the following situation in the form of quadratic equation:

Rohan's mother is $26$ years older than him. The product of their ages after $3$ years will be $360$ years. We need to find Rohan's present age.