Check if it is quadratic . If quadratic, change to standard form and identify a, b and c. X²=2x(6X²+4) 


To determine if the given equation is quadratic and convert it to standard form, we need to first expand and simplify the equation. Let's start with the given equation:

\[ X^2 = 2x(6X^2 + 4) \]

### Step 1: Expand the right side
First, distribute \(2x\) inside the parentheses:

\[ 2x(6X^2 + 4) = 2x \cdot 6X^2 + 2x \cdot 4 \]
\[ = 12X^3 + 8X \]

So the equation becomes:

\[ X^2 = 12X^3 + 8X \]

### Step 2: Bring all terms to one side to form a polynomial equation
Subtract \(12X^3 + 8X\) from both sides to set the equation to zero:

\[ X^2 - 12X^3 - 8X = 0 \]

### Step 3: Check if the equation is quadratic
An equation is quadratic if it can be written in the form:

\[ ax^2 + bx + c = 0 \]

In this case, our equation is:

\[ X^2 - 12X^3 - 8X = 0 \]

This is not a quadratic equation because it contains a term with \(X^3\). A quadratic equation should only have terms up to \(X^2\).

Since the highest power of \(X\) is 3, this is a cubic equation, not a quadratic equation.

### Summary
The given equation is not quadratic because it contains a term with \(X^3\). Therefore, there is no need to change it to standard form or identify \(a\), \(b\), and \(c\) as it does not meet the criteria for a quadratic equation.

Would you like further details or have any questions?

Here are some related questions to explore further:

1. What are the characteristics of a quadratic equation?
2. How can you factor a cubic equation?
3. What are the different methods to solve a cubic equation?
4. How do you identify the degree of a polynomial?
5. What is the significance of the highest degree term in a polynomial equation?
6. Can a cubic equation be simplified to a quadratic equation under certain conditions?
7. What are the general steps to solve polynomial equations of higher degrees?
8. How do polynomial equations differ from linear equations?

**Tip:** When dealing with polynomial equations, always check the highest power of the variable to determine the degree of the equation. This will help you identify the type of polynomial and the appropriate methods to solve it.

Explore how to identify and handle polynomial equations, focusing on a specific example involving quadratic and cubic equations. Includes step-by-step analysis of the given equation X² = 2x(6X² + 4).

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