Check whether the following are quadratic equation
(i) `(x+1)^2=2(x-3)`
(ii) `x^2-2x=(-2)(3-x)`
(iii) `(x-2)(x+1)=(x-1)(x+3)`
(iv) `(x-3)(2x+1)=x(x+5)`
(v) `(2x-1)(x-3)=(x+5)(x-1)`
(vi) `x^2+3x+1=(x-2)^2`
(vii) `(x+2)^3=2x(x^2-1)`
(viii) `x^3-4x^2 – x + 1 = (x – 2)^3`

Explanation

To determine whether each of the given equations is a quadratic equation, we need to simplify each equation and check the degree of the resulting polynomial. A quadratic equation is defined as a polynomial equation of degree 2, which means the highest power of the variable \(x\) should be 2.

Let's analyze each equation step by step.

### (i) \((x+1)^2 = 2(x-3)\)

1. Expand both sides:
\[
...