(a+b)^3+(a-b)^3 Simplify

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Jul 03, 2024

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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.