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Explain the process of multiplying a binomial by an algebraic expression.
Explain the process of multiplying a binomial by an algebraic expression.
To multiply a binomial by an algebraic expression, distribute each term of the binomial to every term of the algebraic expression and then combine like terms.
What are the key steps in multiplying a binomial by an algebraic expression?
What are the key steps in multiplying a binomial by an algebraic expression?
The key steps involve distributing each term of the binomial to every term of the algebraic expression, and then combining like terms.
Can you provide an example of multiplying a binomial by an algebraic expression?
Can you provide an example of multiplying a binomial by an algebraic expression?
Certainly! An example could be (x + 2)(3x - 4), where each term of (x + 2) is distributed to each term of (3x - 4) and then the like terms are combined to simplify the expression.
When multiplying a binomial by an algebraic expression, what is the first step?
When multiplying a binomial by an algebraic expression, what is the first step?
In the process of multiplying a binomial by an algebraic expression, what should be done after distributing each term of the binomial across the terms of the algebraic expression?
In the process of multiplying a binomial by an algebraic expression, what should be done after distributing each term of the binomial across the terms of the algebraic expression?
What is the result of multiplying a binomial by an algebraic expression called?
What is the result of multiplying a binomial by an algebraic expression called?
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Study Notes
Multiplying a Binomial by an Algebraic Expression
- Multiplication involves distributing each term of the binomial to every term in the algebraic expression.
- The binomial is represented as (a + b) or (a - b), where 'a' and 'b' are individual terms.
- Key phrases involved include "distributing" and "combining like terms."
Steps in the Process
- First Step: Begin by applying the distributive property, multiplying each term in the binomial by each term in the algebraic expression.
- After distributing each term, combine like terms to simplify the expression.
- Arranging the resulting terms in standard polynomial form may be necessary.
Example of Multiplying a Binomial
- For instance, multiplying (x + 2) by (3x + 4):
- Distribute: x * 3x + x * 4 + 2 * 3x + 2 * 4.
- Calculate: 3x² + 4x + 6x + 8.
- Combine: 3x² + 10x + 8 is the final result.
Resulting Expression
- The outcome of multiplying a binomial by an algebraic expression is referred to as a polynomial.
- The final polynomial may vary in degree based on the highest exponent present in the result.
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