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 check if the highest power of the variable \( x \) in each equation is 2. A quadratic equation is generally in the form \( ax^2 + bx + c = 0 \), where \( a \neq 0 \).

Let's analyze each equation step by step:

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

1. **Expand both sides**:
\[
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