Podcast
Questions and Answers
A monomial is an algebraic expression consisting of a single ______.
A monomial is an algebraic expression consisting of a single ______.
term
When multiplying monomials, you multiply the ______ and then the variables.
When multiplying monomials, you multiply the ______ and then the variables.
coefficients
When multiplying variables with the same base, you ______ the exponents.
When multiplying variables with the same base, you ______ the exponents.
add
The result of multiplying the coefficients in the expression (3x²) * (2x³) is ______.
The result of multiplying the coefficients in the expression (3x²) * (2x³) is ______.
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Any variable raised to the zero power equals ______.
Any variable raised to the zero power equals ______.
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In the example (-2a²b) * (5a³b²), the combined result for the coefficients is ______.
In the example (-2a²b) * (5a³b²), the combined result for the coefficients is ______.
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If a monomial includes a variable with a negative exponent, you can ______ the base.
If a monomial includes a variable with a negative exponent, you can ______ the base.
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The order in which monomials are multiplied does not affect the result because multiplication is ______.
The order in which monomials are multiplied does not affect the result because multiplication is ______.
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Study Notes
Multiplying Monomials
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A monomial is an algebraic expression consisting of a single term, which may be a number, a variable, or a product of a number and one or more variables. Examples include 5, x, 3y, and 4x².
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When multiplying monomials, you multiply the coefficients (the numerical parts) and then the variables.
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Multiplying Coefficients: Simply multiply the numerical values of the coefficients.
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Multiplying Variables: Multiply the variables together. If a variable appears in multiple monomials being multiplied, add the exponents. This is based on the rule: xm * xn = x(m+n)
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Example 1: Multiply (3x²) * (2x3)
- Multiply the coefficients: 3 * 2 = 6
- Multiply the variables: x² * x3 = x(2+3) = x5
- Combine the results: 6x5
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Example 2: Multiply (4y) * (5y²) * (2y³)
- Multiply the coefficients: 4 * 5 * 2 = 40
- Multiply the variables: y * y² * y³ = y(1+2+3) = y6
- Combine the results: 40y6
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Adding Exponents ONLY when multiplying with the same base: When multiplying variables with the same base, add the exponents. This is a fundamental rule for simplifying expressions involving products of variables.
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Example 3: Multiply ( −2a2b) * (5a3b2)
- Multiply the coefficients: -2 * 5 = -10
- Multiply the variables: a2 * a3 = a(2+3)= a5 and b * b2 = b(1+2)=b3
- Combine the results: -10a5b3
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Order of Operations: Within a product of monomials, the order in which the monomials are multiplied does not affect the result as the multiplication operation is commutative.
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Zero Exponent Rule: Any variable raised to the zero power equals 1 (except for zero). For example, x0 = 1, y0 = 1, etc.
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Important Note on Negative Exponents: If a monomial includes a variable with a negative exponent, you can reciprocate the base and change the sign of the exponent to make the exponent positive. For Example: x-n = 1/xn
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Example 4: Find the product of (-3x-5) and (2x3).
- Multiply the coefficients: -3 * 2 = -6
- Multiply the variables: x-5 * x3 = x(-5+3) = x-2
- Combining coefficients and variables will give you: -6x-2
- Rewrite with a positive exponent: -6/x²
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Description
Test your knowledge on multiplying monomials in algebra. This quiz covers the fundamental rules for multiplying coefficients and variables, including how to handle exponents. Get ready to apply what you've learned with practical examples.
