(2b^3-5b)-(7b+3b^2)

Jasonbradley

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Jun 16, 2024

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Simplifying the Expression: (2b^3 - 5b) - (7b + 3b^2)

This article aims to guide you through the process of simplifying the algebraic expression: (2b^3 - 5b) - (7b + 3b^2).

Understanding the Expression

The expression involves variables, coefficients, and exponents. Let's break it down:

• Variables: The letter "b" represents a variable, which can take on different values.
• Coefficients: The numbers 2, -5, -7, and 3 are coefficients, which multiply the variables.
• Exponents: The number 3 in 2b^3 and 3b^2 indicates the power to which the variable "b" is raised.

Simplifying the Expression

1. Distribute the negative sign: The minus sign before the second set of parentheses means we multiply each term inside the parentheses by -1. This gives us:

   (2b^3 - 5b) + (-7b - 3b^2)

2. Combine like terms: Like terms have the same variable and exponent.

   • b^3 terms: There's only one term with b^3, 2b^3.
   • b^2 terms: We have -3b^2.
   • b terms: We have -5b and -7b, which combine to -12b.

3. Rearrange in descending order of exponents:

   2b^3 - 3b^2 - 12b

Final Simplified Expression

The simplified form of the expression (2b^3 - 5b) - (7b + 3b^2) is 2b^3 - 3b^2 - 12b.