Difference of squares intro | Mathematics II | High School Math | Khan Academy

TL;DR

Factoring a difference of squares involves subtracting two quantities that are each squares, and it can be easily done by using the pattern (x + a)(x - a) = x^2 - a^2.

Transcript

• [Instructor] We're now going to explore factoring a type of expression called a difference of squares and the reason why it's called a difference of squares is 'cause it's expressions like x squared minus nine. This is a difference. We're subtracting between two quantities that are each squares. This is literally x squared. Let me do that in a di... Read More

Key Insights

• ❎ A difference of squares involves subtracting two quantities that are each squares.
• ☺️ The pattern for factoring a difference of squares is (x + a)(x - a) = x^2 - a^2.
• 🍉 The "a" term in the factoring pattern represents the square root of the number being subtracted.
• ❎ Both numeric perfect squares and variables that can be square rooted can be used in a difference of squares expression.
• ❎ Recognizing the things that are being squared is crucial in correctly factoring a difference of squares.
• ❎ Common mistakes include incorrectly identifying the squared terms or attempting to factor a sum of squares instead.
• 🏃 Khan Academy offers practice exercises to improve familiarity with factoring difference of squares.

Questions & Answers

Q: What is a difference of squares?

A difference of squares is an expression where two quantities, whether they are numeric perfect squares or variables that can be square rooted, are subtracted from each other.

Q: How can a difference of squares be factored?

A difference of squares can be factored by using the pattern (x + a)(x - a) = x^2 - a^2, where "a" represents the square root of the number being subtracted.

Q: Why is it important to identify the things that are being squared in a difference of squares?

It is important to recognize what is getting squared in a difference of squares because that determines the terms to be used in the factoring process, such as (x + a)(x - a) or (y + a)(y - a).

Q: Can the difference of squares pattern be used for any difference of squares expression?

Yes, the pattern (x + a)(x - a) = x^2 - a^2 can be applied to any difference of squares expression, as long as it follows the format of subtracting one squared quantity from another.

Summary & Key Takeaways

• A difference of squares is an expression that involves subtracting two quantities that are each squares, such as x^2 - 9.

• To factor a difference of squares, you can use the pattern (x + a)(x - a) = x^2 - a^2, where "a" represents the square root of the number being subtracted.

• The pattern can be applied to any difference of squares, whether it involves numeric perfect squares or variables that can be square rooted.