Factoring Sums and Differences of Perfect Cubes | Summary and Q&A

TL;DR

Learn how to factor expressions that involve sums and differences of cubes using a specific formula.

Key Insights

• 👶 The formula for factoring sums of cubes is a + b (a² - ab + b²), while the formula for factoring differences of cubes is a - b (a² + ab + b²).
• 🥡 Identifying the values of a and b by taking the cube root of the given expressions is crucial.
• ✊ The cube root of a number represents the value that, when raised to the power of 3, gives the original number.
• ❣️ Factors such as x, y, numbers, and their combinations can be used as variables for a and b.

Transcript

in this video we're going to focus on factoring sums and difference of cubes so let's say if we want to factor the expression x cubed plus 8. now there is an equation that you want to use and here it is a to the third plus b to the third this is equal to uh a plus b times uh a squared minus a b plus b squared so you need to realize that a to the th... Read More

Questions & Answers

Q: How do you factor an expression that involves sums of cubes?

To factor a sum of cubes, identify the values of a and b by taking the cube root of the given expressions. Then plug these values into the formula a + b (a² - ab + b²) to obtain the factored expression.

Q: Can you provide an example of factoring a sum of cubes?

Sure! Let's factor the expression x³ + 8. By taking the cube root of x³, we get a = x. The cube root of 8 is 2, giving us b = 2. Plugging these values into the formula, we have (x + 2)(x² - 2x + 4) as the factored expression.

Q: How do you factor an expression that involves differences of cubes?

To factor a difference of cubes, identify the values of a and b by taking the cube root of the given expressions. Then plug these values into the formula a - b (a² + ab + b²) to obtain the factored expression.

Q: Can you provide an example of factoring a difference of cubes?

Certainly! Let's factor the expression x³ - 125. By taking the cube root of x³, we find a = x. The cube root of 125 is 5, giving us b = 5. Plugging these values into the formula, we have (x - 5)(x² + 5x + 25) as the factored expression.

Summary & Key Takeaways

• The video teaches how to factor expressions that involve sums and differences of cubes using a specific equation.

• To factor a sum of cubes, identify the values of a and b by taking the cube root of the given expressions. Plug these values into the formula to obtain the factored expression.

• The same process applies to factor a difference of cubes, but with a change in the sign between a and b in the formula.