Simplifying Algebraic Expressions: (5b + 6b³) + (7b³ + 8b)
This article will guide you through the process of simplifying the algebraic expression (5b + 6b³) + (7b³ + 8b).
Understanding the Expression
The expression consists of four terms:
 5b: A term with a coefficient of 5 and variable 'b' raised to the power of 1.
 6b³: A term with a coefficient of 6 and variable 'b' raised to the power of 3.
 7b³: A term with a coefficient of 7 and variable 'b' raised to the power of 3.
 8b: A term with a coefficient of 8 and variable 'b' raised to the power of 1.
Simplifying the Expression
To simplify, we combine like terms:

Identify like terms: The terms 5b and 8b are like terms because they have the same variable 'b' raised to the same power (1). Similarly, 6b³ and 7b³ are like terms because they have the same variable 'b' raised to the same power (3).

Combine like terms: Add the coefficients of the like terms:
 5b + 8b = 13b
 6b³ + 7b³ = 13b³

Write the simplified expression: The simplified expression is 13b³ + 13b.
Conclusion
By combining like terms, we have simplified the expression (5b + 6b³) + (7b³ + 8b) to 13b³ + 13b. This process is essential in algebra for manipulating and solving equations.