(5b^3-6b^4-b^2-7b)-(7b-2b^4-7b^3+b^2)-(2b^3+5b)

Jasonbradley

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Jun 16, 2024

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Simplifying Polynomial Expressions

This article will guide you through simplifying the following polynomial expression:

(5b^3-6b^4-b^2-7b)-(7b-2b^4-7b^3+b^2)-(2b^3+5b)

Understanding the Basics

Before we start simplifying, let's refresh our understanding of polynomials:

• Polynomials: Algebraic expressions containing variables and constants combined using addition, subtraction, and multiplication.
• Terms: Parts of a polynomial separated by addition or subtraction.
• Coefficients: Numerical factors in front of variables.
• Variables: Letters representing unknown values (like 'b' in our expression).
• Exponents: Small numbers written above and to the right of a variable, indicating how many times the variable is multiplied by itself.

Step-by-Step Simplification

1. Remove Parentheses: Start by removing the parentheses. Remember that a minus sign before a parenthesis changes the sign of each term inside:

   5b^3 - 6b^4 - b^2 - 7b - 7b + 2b^4 + 7b^3 - b^2 - 2b^3 - 5b 
   

2. Combine Like Terms: Identify terms with the same variable and exponent (like terms) and combine their coefficients:

   • b^4 terms: -6b^4 + 2b^4 = -4b^4
   • b^3 terms: 5b^3 + 7b^3 - 2b^3 = 10b^3
   • b^2 terms: -b^2 - b^2 = -2b^2
   • b terms: -7b - 7b - 5b = -19b

3. Write the Simplified Expression: Combine the results from step 2 to get the simplified polynomial:

   -4b^4 + 10b^3 - 2b^2 - 19b
   

Conclusion

The simplified form of the expression (5b^3-6b^4-b^2-7b)-(7b-2b^4-7b^3+b^2)-(2b^3+5b) is -4b^4 + 10b^3 - 2b^2 - 19b.

By following the steps of removing parentheses and combining like terms, we've successfully simplified the expression. Remember, understanding the basics of polynomials is crucial for simplifying complex expressions.