Factoring Binomials With Exponents, Difference of Squares & Sum of Cubes, 2 Variables - Algebra

TL;DR

Learn how to factor binomial expressions by removing the greatest common factor and using the difference of squares or cubes methods.

Transcript

in this video we're going to focus on factoring binomials so binomial is basically a polynomial with two terms so let's say if we have the expression x squared plus 4x what can we do to factor this particular expression the first thing you should look for always is to remove the gcf the greatest common factor the greatest common factor between x sq... Read More

Key Insights

• 🧑‍🏭 Factoring binomial expressions involves removing the greatest common factor (GCF) first.
• ❎ The difference of squares technique is used when the expression consists of two perfect squares with a subtraction sign.
• 😑 The difference of cubes technique is applied when the expression is in the form of a³ - b³.
• 🧑‍🏭 Factoring can be simplified by factoring out the GCF before applying other factoring techniques.
• 🧊 The cube root is used to find a and b in the difference of cubes technique.
• 💁 The solutions involve both adding and subtracting terms in the factored form.
• 🧊 Sometimes no GCF is present, and direct application of the difference of squares or cubes method is required.

Questions & Answers

Q: What is the first step in factoring binomials?

The first step is to look for the greatest common factor (GCF) and divide both terms by it. This simplifies the expression before applying any further factoring techniques.

Q: How is the difference of squares technique used in factoring?

To use the difference of squares technique, identify two terms that are perfect squares (e.g., x² and 25) and apply the formula: a² - b² = (a - b)(a + b).

Q: What is the difference of cubes technique?

The difference of cubes technique is used when factoring expressions that are in the form a³ - b³. Applying the formula: a³ - b³ = (a - b)(a² + ab + b²), where a and b are both cube roots of the respective terms.

Q: Can you explain how to factor x³ - 8?

This expression can be factored using the difference of cubes technique. The cube root of x³ is x, and the cube root of 8 is 2. Thus, the final factored form is (x - 2)(x² + 2x + 4).

Summary & Key Takeaways

• The video teaches how to factor binomials by removing the greatest common factor (GCF) first before applying the difference of squares or cubes techniques.

• Examples are provided to demonstrate the process of factoring using the GCF and the difference of squares or cubes methods.

• The video covers various scenarios, including cases where no GCF is present and where the expressions involve variables raised to different exponents.