Expanding 3(x+h)^3 ================::::::::
In algebra, expanding an expression involving powers of a binomial, such as 3(x+h)^3, can be a bit challenging. However, with the right approach and formula, it's definitely doable. In this article, we'll explore how to expand 3(x+h)^3 using the binomial theorem.
The Binomial Theorem
The binomial theorem is a mathematical formula that describes the expansion of powers of a binomial expression. It's stated as follows:
(a+b)^n = a^n + na^(n-1)b + n(n-1)a^(n-2)b^2 + ... + b^n
In our case, we have 3(x+h)^3, where a = x, b = h, and n = 3. Let's plug these values into the formula and see what we get.
Expanding 3(x+h)^3
Using the binomial theorem, we can expand 3(x+h)^3 as follows:
3(x+h)^3 = 3(x^3 + 3x^2h + 3xh^2 + h^3)
Now, let's break down each term in the expansion:
x^3
This is the first term in the expansion, which is obtained by raising x to the power of 3.
3x^2h
This term is obtained by multiplying x^2 by h, and then multiplying the result by 3.
3xh^2
This term is obtained by multiplying x by h^2, and then multiplying the result by 3.
h^3
This is the last term in the expansion, which is obtained by raising h to the power of 3.
Simplifying the Expansion
Now that we have the expansion, we can simplify it by combining like terms:
3(x+h)^3 = 3x^3 + 9x^2h + 9xh^2 + 3h^3
And that's the final answer! We've successfully expanded 3(x+h)^3 using the binomial theorem.
Conclusion
Expanding powers of binomials can be a bit challenging, but with the right approach and formula, it's definitely doable. In this article, we've explored how to expand 3(x+h)^3 using the binomial theorem. We hope this helps you in your algebraic endeavors!
