%5E3-simplify.jpeg "(a+b)^3 Simplify")
(a+b)^3 Simplified
The cube of a binomial, (a+b)^3, is a mathematical expression that can be simplified using the rules of algebra. In this article, we will explore the process of simplifying (a+b)^3 and provide the final result.
The Expression (a+b)^3
The expression (a+b)^3 is a binomial raised to the power of 3. It can be expanded using the rule of exponents, which states that (a+b)^3 = (a+b) × (a+b) × (a+b).
Expanding the Expression
To expand the expression, we need to multiply the three binomials together. This can be done using the distributive property of multiplication over addition.
(a+b) × (a+b) × (a+b) = a × (a+b) × (a+b) + b × (a+b) × (a+b)
= a × (a^2 + 2ab + b^2) + b × (a^2 + 2ab + b^2)
Simplifying the Expression
Now, we can simplify the expression by combining like terms.
= a^3 + 2a^2b + ab^2 + a^2b + 2ab^2 + b^3
= a^3 + 3a^2b + 3ab^2 + b^3
The Final Result
The simplified expression for (a+b)^3 is:
(a+b)^3 = a^3 + 3a^2b + 3ab^2 + b^3
This expression is a cubic polynomial with four terms, each with a different power of a and b.
Conclusion
In this article, we have simplified the expression (a+b)^3 using the rules of algebra. The final result is a cubic polynomial with four terms. This expression is commonly used in algebra and calculus to solve problems involving cubics and polynomials.
