Check whether the following are quadratic equations :
(x - 3) (x - 3) = (x + 5) (x - 1)

Answer

To check whether the given equation \((x - 3)(x - 3) = (x + 5)(x - 1)\) is a quadratic equation, we will follow these steps:

### Step 1: Expand both sides of the equation
We start by expanding the left-hand side and the right-hand side.

- Left-hand side:
\[ (x - 3)(x - 3) = (x - 3)^2 = x^2 - 6x + 9 \]

- Right-hand side:
\[ (x + 5)(x - 1) = x^2 - x + 5x - 5 = x^2 + 4x - 5 \]

### Step 2: Set the equation
Now we can set the expanded forms equal to each other:
\[ x^2 - 6x + 9 = x^2 + 4x - 5 \]

### Step 3: Move all terms to one side
Next, we will move all terms to one side of the equation to simplify it:
\[ x^2 - 6x + 9 - x^2 - 4x + 5 = 0 \]
This simplifies to:
\[ -10x + 14 = 0 \]

### Step 4: Rearranging the equation
Now, rearranging gives:
\[ 10x - 14 = 0 \]

### Step 5: Identify the coefficients
In the equation \(10x - 14 = 0\), we can see that there is no \(x^2\) term. The standard form of a quadratic equation is \(ax^2 + bx + c = 0\) where \(a \neq 0\). Here, \(a = 0\), \(b = 10\), and \(c = -14\).

### Conclusion
Since the coefficient \(a\) of \(x^2\) is zero, the equation \(10x - 14 = 0\) is not a quadratic equation.

### Final Answer
Thus, the equation \((x - 3)(x - 3) = (x + 5)(x - 1)\) is **not a quadratic equation**.

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