(5ab%5E2)-(a%5E5b%5E2)(9b).jpeg "(3a^4b)(5ab^2)-(a^5b^2)(9b)")
Simplifying Algebraic Expressions: (3a^4b)(5ab^2)-(a^5b^2)(9b)
This article will guide you through the process of simplifying the algebraic expression: (3a^4b)(5ab^2)-(a^5b^2)(9b).
Understanding the Basics
Before we dive into the simplification, let's review some fundamental concepts:
- Variables: Letters like 'a' and 'b' represent unknown values.
- Coefficients: Numbers in front of variables like '3' and '5' indicate how many times the variable is multiplied by itself.
- Exponents: Small numbers written above and to the right of a variable (e.g., a^4) indicate how many times the variable is multiplied by itself.
Simplifying the Expression
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Apply the Distributive Property:
- Multiply the terms inside each set of parentheses:
- (3a^4b)(5ab^2) = 15a^5b^3
- (a^5b^2)(9b) = 9a^5b^3
- Multiply the terms inside each set of parentheses:
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Combine Like Terms:
- Since both terms now have the same variables and exponents (a^5b^3), we can subtract their coefficients:
- 15a^5b^3 - 9a^5b^3 = 6a^5b^3
- Since both terms now have the same variables and exponents (a^5b^3), we can subtract their coefficients:
Final Result
Therefore, the simplified form of the expression (3a^4b)(5ab^2)-(a^5b^2)(9b) is 6a^5b^3.
Key Takeaway
Simplifying algebraic expressions involves applying basic arithmetic operations and utilizing the properties of exponents. By carefully combining like terms and using the distributive property, you can efficiently simplify complex expressions into a more manageable form.