%2B(7b%5E3%2B8b).jpeg "(5b+6b^3)+(7b^3+8b)")
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:
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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).
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Combine like terms: Add the coefficients of the like terms:
- 5b + 8b = 13b
- 6b³ + 7b³ = 13b³
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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.