Question
Match the terms to their definition. 1. distributive property \( \begin{array}{l}\text { 2. like terms } \\ \text { 3. polynomial } \\ \text { variables have whole number exponents } \\ \text { varms that have the same }\end{array} \) variable(s). with each variable raised to \( +a c o r a(b-c)=a b-a c \) the same exponent
Ask by Mills Schneider.
Feb 27,2025 07:10
UpStudy AI Solution
Tutor-Verified Answer
Answer
1. Distributive Property: \( a(b - c) = ab - ac \)
2. Like Terms: terms that have the same variable(s) with each variable raised to the same exponent
3. Polynomial: variables have whole number exponents
Solution
Let's match the terms to their definitions step by step.
1. **Distributive Property**: This property states that \( a(b - c) = ab - ac \). It allows you to distribute a multiplication over addition or subtraction.
2. **Like Terms**: These are terms that have the same variable(s) with each variable raised to the same exponent. For example, \( 3x^2 \) and \( 5x^2 \) are like terms.
3. **Polynomial**: A polynomial is an expression that consists of variables raised to whole number exponents and combined using addition, subtraction, and multiplication.
Now, let's match them:
- **Distributive Property**: \( a(b - c) = ab - ac \)
- **Like Terms**: terms that have the same variable(s) with each variable raised to the same exponent
- **Polynomial**: variables have whole number exponents
So the final matches are:
1. Distributive Property: \( a(b - c) = ab - ac \)
2. Like Terms: terms that have the same variable(s) with each variable raised to the same exponent
3. Polynomial: variables have whole number exponents
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Simplify this solution Extra Insights
The distributive property states that when you multiply a number by a sum, you can distribute the multiplication across the terms inside the parentheses. For example, \( a(b - c) = ab - ac \). It’s a handy property that makes calculations much clearer and helps in simplifying expressions with ease!
Like terms are terms in an algebraic expression that have the same variables raised to the same powers. This means you can combine them when simplifying expressions or performing operations. For instance, \( 3x^2 \) and \( 5x^2 \) are like terms, but \( 2xy \) and \( 4x^2 \) are not, as they involve different variables!
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