Expand (x²-5x+6)⁴ 2 Through Multinomial Theorem

To expand \((x^2 - 5x + 6)^4\) using the **Multinomial Theorem**, we need to express the expansion as a sum of products of powers of each term in the polynomial, based on the multinomial formula.

The **Multinomial Theorem** for \((x_1 + x_2 + \cdots + x_m)^n\) states:

\[
(x_1 + x_2 + \cdots + x_m)^n = \sum_{k_1+k_2+\cdots+k_m=n} \binom{n}{k_1, k_2, \ldots, k_m} x_1^{k_1} x_2^{k_2} \cdots x_m^{k_m}
\]

Where:
- \( \binom{n}{k_1, k_2, \ldots, k_m} \) is the multinomial coefficient, given by:

\[
\binom{n}{k_1, k_2, \ldots, k_m} = \frac{n!}{k_1

Explore how to expand the expression (x²-5x+6)⁴ using the Multinomial Theorem. This solution involves advanced algebraic concepts and provides a step-by-step explanation for expanding polynomials. Ideal for students in Grades 11-12 or early college.

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