%5E3-expand-formula.jpeg "(x+2)^3 Expand Formula")
Expanding (x+2)^3 using the Binomial Theorem
In algebra, the binomial theorem is a powerful tool for expanding expressions of the form (x + y)^n, where n is a positive integer. In this article, we will explore how to expand the expression (x + 2)^3 using the binomial theorem.
The Binomial Theorem
The binomial theorem states that:
(x + y)^n = x^n + nx^(n-1)y + n(n-1)x^(n-2)y^2 + … + nx^y^(n-1) + y^n
where n is a positive integer, and x and y are variables.
Expanding (x + 2)^3
To expand (x + 2)^3, we can plug in x = x and y = 2 into the binomial theorem formula, where n = 3. This gives us:
(x + 2)^3 = x^3 + 3x^2(2) + 3x(2)^2 + (2)^3
Simplifying the Expression
Now, let's simplify the expression by evaluating the powers and multiplying the terms:
(x + 2)^3 = x^3 + 6x^2 + 12x + 8
And that's the expanded form of (x + 2)^3!
Conclusion
In conclusion, we have successfully expanded the expression (x + 2)^3 using the binomial theorem. This formula can be applied to any binomial expression of the form (x + y)^n, where n is a positive integer. With practice and patience, you'll become proficient in expanding binomial expressions and tackling more complex algebraic problems.
