Multiplying Polynomials - Math Tutorial
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1 year ago
Published on Apr 22, 2024
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Table of Contents
Tutorial: Multiplying Polynomials using the FOIL Technique
Step 1: Introduction to the FOIL Technique
- The FOIL technique stands for First, Outer, Inner, Last, and is used to multiply two binomials.
- The first step is to identify the first, outer, inner, and last terms in each binomial.
Step 2: Identify the Terms
- The first terms are the first two terms in each binomial.
- The outer terms are the terms on the outer edges of the expression.
- The inner terms are the terms on the inside of the expression.
- The last terms are the last two terms in each binomial.
Step 3: Apply the FOIL Technique
- Multiply the first terms: Multiply the first term of the first binomial by the first term of the second binomial.
- Multiply the outer terms: Multiply the outer terms of the expression.
- Multiply the inner terms: Multiply the inner terms of the expression.
- Multiply the last terms: Multiply the last term of the first binomial by the last term of the second binomial.
Step 4: Perform the Multiplications
- For example, if given (-x^2 - x)(x + 5), apply the FOIL technique as follows:
- First: (-x^2) * (x) = -x^3
- Outer: (-x^2) * (5) = -5x^2
- Inner: (-x) * (x) = -x^2
- Last: (-x) * (5) = -5x
Step 5: Combine the Results
- Write out the results of each multiplication step.
- Combine like terms if applicable.
- Arrange the terms in descending order of exponents.
Step 6: Finalize the Result
- After combining like terms, the final result should be in the form of a polynomial.
- Check for any common terms that can be further simplified or combined.
By following these steps, you can effectively multiply polynomials using the FOIL technique as demonstrated in the tutorial video by Brian McLogan.