%5E3-(a-b)%5E3-simplify.jpeg "(a+b)^3-(a-b)^3 Simplify")
(a+b)^3-(a-b)^3 Simplified
In this article, we will simplify the algebraic expression (a+b)^3-(a-b)^3. To do this, we need to understand the cube of a binomial and how to expand it.
Expanding the Cubes
The cube of a binomial can be expanded using the formula:
(a+b)^3 = a^3 + 3a^2b + 3ab^2 + b^3
Similarly, we can expand (a-b)^3 as:
(a-b)^3 = a^3 - 3a^2b + 3ab^2 - b^3
Simplifying the Expression
Now, let's simplify the given expression:
(a+b)^3-(a-b)^3
Substitute the expanded expressions for (a+b)^3 and (a-b)^3:
= (a^3 + 3a^2b + 3ab^2 + b^3) - (a^3 - 3a^2b + 3ab^2 - b^3)
Combine Like Terms
Combine the like terms:
= a^3 + 3a^2b + 3ab^2 + b^3 - a^3 + 3a^2b - 3ab^2 + b^3
Simplify the expression by combining the like terms:
= **12ab^2**
Therefore, the simplified expression for (a+b)^3-(a-b)^3 is 12ab^2.
