%5E6-binomial-expansion.jpeg "(2x-3)^6 Binomial Expansion")
Binomial Expansion of (2x-3)^6
In this article, we will explore the binomial expansion of (2x-3)^6, which is a mathematical expression that involves the power of a binomial expression.
What is Binomial Expansion?
Binomial expansion is a method of expanding powers of a binomial expression, which is an expression consisting of two terms. The general formula for binomial expansion is:
$(a+b)^n = \sum_{k=0}^n \binom{n}{k} a^{n-k} b^k$
where n is a positive integer, a and b are constants, and $\binom{n}{k}$ is the binomial coefficient.
Binomial Expansion of (2x-3)^6
To expand (2x-3)^6, we can use the binomial expansion formula with a = 2x and b = -3. We get:
$(2x-3)^6 = \sum_{k=0}^6 \binom{6}{k} (2x)^{6-k} (-3)^k$
Now, we can simplify the expression by calculating the binomial coefficients and expanding the powers:
$(2x-3)^6 = \binom{6}{0} (2x)^6 (-3)^0 + \binom{6}{1} (2x)^5 (-3)^1 + \binom{6}{2} (2x)^4 (-3)^2 + \binom{6}{3} (2x)^3 (-3)^3 + \binom{6}{4} (2x)^2 (-3)^4 + \binom{6}{5} (2x)^1 (-3)^5 + \binom{6}{6} (2x)^0 (-3)^6$
Simplifying further, we get:
$(2x-3)^6 = 64x^6 - 576x^5 + 2160x^4 - 4320x^3 + 3888x^2 - 1728x + 729$
Conclusion
In this article, we have seen how to expand the binomial expression (2x-3)^6 using the binomial expansion formula. The result is a polynomial expression with seven terms. Binomial expansion is a powerful tool in algebra and is used in many mathematical and scientific applications.
