%5E3-expanded.jpeg "(2+x)^3 Expanded")
(2+x)^3 Expanded
In algebra, expanding an expression involving exponents and variables is a crucial skill to master. One such expression is (2+x)^3, which we will expand in this article.
The Formula
Before we dive into the expansion, let's recall the formula for expanding a binomial expression raised to a power of 3:
(a+b)^3 = a^3 + 3a^2b + 3ab^2 + b^3
In our case, we have a = 2 and b = x.
Expanding (2+x)^3
Using the formula above, we can expand (2+x)^3 as follows:
(2+x)^3 = 2^3 + 3(2^2)(x) + 3(2)(x^2) + x^3
Simplifying the Expression
Let's simplify the expression by evaluating the exponents and combining like terms:
2^3 = 8
3(2^2)(x) = 3(4)(x) = 12x
3(2)(x^2) = 6x^2
x^3 = x^3
So, the expanded expression is:
(2+x)^3 = 8 + 12x + 6x^2 + x^3
And that's it! We have successfully expanded (2+x)^3.
Conclusion
Expanding expressions involving exponents and variables may seem daunting at first, but with the right formula and a bit of practice, it can become second nature. In this article, we have expanded (2+x)^3 using the formula for binomial expressions raised to a power of 3. The final result is a quadratic expression with terms involving x and its powers.
