Simplifying Polynomial Expressions
This article will guide you through simplifying the following polynomial expression:
(5b^36b^4b^27b)(7b2b^47b^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.
StepbyStep Simplification

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

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

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^36b^4b^27b)(7b2b^47b^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.