Simplifying (a+b)^3 + (a-b)^3
In algebra, simplifying expressions is an essential skill to master. In this article, we will explore how to simplify the expression (a+b)^3 + (a-b)^3
.
Expansion of Cubes
Before we dive into the simplification, let's recall the formula for expanding cubes:
(a+b)^3 = a^3 + 3a^2b + 3ab^2 + b^3
(a-b)^3 = a^3 - 3a^2b + 3ab^2 - b^3
Simplification
Now, let's simplify the given expression:
(a+b)^3 + (a-b)^3
= (a^3 + 3a^2b + 3ab^2 + b^3) + (a^3 - 3a^2b + 3ab^2 - b^3)
Combine like terms
Now, we combine like terms:
= a^3 + 3a^2b + 3ab^2 + b^3 + a^3 - 3a^2b + 3ab^2 - b^3
= 2a^3 + 6ab^2
Final Simplified Form
The final simplified form of the expression (a+b)^3 + (a-b)^3
is:
2a^3 + 6ab^2
In conclusion, simplifying (a+b)^3 + (a-b)^3
involves expanding the cubes using the formula and then combining like terms to arrive at the final simplified form, 2a^3 + 6ab^2
.