Let coefficient of x4 and x2 in the expansion of  is α and β then α – β is  equal to

Break Down the Problem

1. Identify the polynomial to be expanded.
2. Determine how to extract the coefficients for $x^4$ (denoted as $\alpha$) and $x^2$ (denoted as $\beta$).
3. Calculate the difference $\alpha - \beta$.

Relevant Concepts

1. Binomial Theorem: This theorem will help us expand expressions of the form $(a + b)^n$.
2. Identify terms that yield the coefficients for $x^4$ and $x^2$.

Analysis and Detail

• Without the specific polynomial, I can't perform the calculations. Generally, if you have a polynomial of the form $(x + c)^n$, using the binomial expansion, the coefficients of $x^k$ can be determined using: $\text{Coefficient of } x^k = \binom{n}{k} c^{n-k}$
• For the coefficients $\alpha$ and $\beta$:
  • For $x^4$: $\alpha = \binom{n}{4} c^{n-4}$
  • For $x^2$: $\beta = \binom{n}{2} c^{n-2}$

Verify and Summarize

• Proceed to calculate $\alpha - \beta$: $\alpha - \beta = \left(\binom{n}{4} c^{n-4} - \binom{n}{2} c^{n-2}\right)$

Final Answer

The expression for $\alpha - \beta$ is: $\alpha - \beta = \binom{n}{4} c^{n-4} - \binom{n}{2} c^{n-2}$ Please replace $c$ and $n$ with their specific values from the polynomial, if provided, to obtain a concrete numerical result.