(-2y).jpeg "(3xy^3)(-2y)")
Simplifying Algebraic Expressions: (3xy^3)(-2y)
In algebra, simplifying expressions involves combining like terms and applying the rules of exponents. Let's break down how to simplify the expression (3xy^3)(-2y).
Understanding the Components
- Coefficients: These are the numerical values in front of the variables. In our expression, we have 3 and -2.
- Variables: These are letters representing unknown quantities. Here, we have x and y.
- Exponents: These small numbers written above the variables indicate how many times the variable is multiplied by itself. We have y^3 and y^1 (remember that a variable without an exponent is understood to have an exponent of 1).
Applying the Rules
- Multiply the coefficients: 3 * -2 = -6
- Combine the variables: x remains unchanged.
- Apply the rule for multiplying exponents: When multiplying variables with the same base, add their exponents. Therefore, y^3 * y^1 = y^(3+1) = y^4
The Simplified Expression
Putting it all together, the simplified form of (3xy^3)(-2y) is -6xy^4.
Key Points to Remember
- Order of Operations: Always follow the order of operations (PEMDAS/BODMAS) when simplifying expressions.
- Combining Like Terms: You can only combine terms that have the same variables and exponents.
- Exponents: Remember the rules for multiplying and dividing exponents.
By understanding the fundamental rules of algebra, you can confidently simplify even complex expressions.