%5E5-binomial-expansion.jpeg "(x-2y)^5 Binomial Expansion")
Binomial Expansion of (x-2y)^5
In algebra, binomial expansion is a method of expanding a binomial expression raised to a power. In this article, we will discuss the binomial expansion of (x-2y)^5.
What is Binomial Expansion?
Binomial expansion is a method of expanding a binomial expression of the form (a+b)^n, where a and b are variables and n is a positive integer. The expansion is based on the formula:
(a+b)^n = a^n + na^(n-1)b + n(n-1)a^(n-2)b^2 + ... + n(n-1)(n-2)...(2)a^1b^(n-1) + b^n
This formula is known as the binomial theorem.
Binomial Expansion of (x-2y)^5
To expand (x-2y)^5, we can use the binomial theorem with a = x, b = -2y, and n = 5. The expansion is as follows:
(x-2y)^5 = x^5 - 5x^4(2y) + 10x^3(2y)^2 - 10x^2(2y)^3 + 5x(2y)^4 - (2y)^5
= x^5 - 10x^4y + 40x^3y^2 - 80x^2y^3 + 80xy^4 - 32y^5
Simplifying the Expansion
The expanded form of (x-2y)^5 is a polynomial expression with six terms. We can simplify the expression by combining like terms:
= x^5 - 10x^4y + 40x^3y^2 - 80x^2y^3 + 80xy^4 - 32y^5
Conclusion
In this article, we have discussed the binomial expansion of (x-2y)^5 using the binomial theorem. We have expanded the expression and simplified it to obtain a polynomial expression with six terms. Binomial expansion is an important concept in algebra and is used in various applications in mathematics, physics, and engineering.
