Factoring the Difference of Two Perfect Squares

This video tutorial teaches how to factor a difference of two squares, a method used in algebra to simplify expressions. The lesson begins by defining the concept, explaining that it involves subtracting one perfect square from another. The instructor demonstrates the factoring process using a sum and difference pattern, where the square roots of the terms are used to form binomials. Several examples are provided, ranging from simple to more complex cases involving multiple variables. The video concludes with a preview of the next lesson on factoring polynomials completely, offering a worksheet for practice.

What does the term 'difference' signify in the context of factoring a difference of two squares?

• Multiplying two squares

• Subtracting two squares

• Adding two squares

• Dividing two squares

In the pattern (a - b)(a + b), what do 'a' and 'b' represent?

• The constants in the equation

• The coefficients of the terms

• The square roots of the perfect squares

• The exponents of the terms

Why do the middle terms cancel out when you distribute (a - b)(a + b)?

• Because one is positive and one is negative

• Because they are both negative

• Because they are both positive

• Because they are both zero

What is the factored form of x^2 - 100?

• (x - 10)(x + 20)

• (x - 10)(x - 10)

• (x + 10)(x + 10)

• (x + 10)(x - 10)

What is the square root of 4y^2?

• 2y

• 4y

• y

• 8y

Which of the following is a perfect square?

• 30

• 35

• 25

• 20

What is the factored form of d^2 - 1?

• (d + 1)(d + 1)

• (d - 1)(d - 1)

• (d + 1)(d - 1)

• (d - 1)(d + 2)

What is the factored form of 16y^2 - 49z^2?

• (4y + 7z)(4y - 7z)

• (4y - 7z)(4y + 14z)

• (4y - 7z)(4y - 7z)

• (4y + 7z)(4y + 7z)

What is the factored form of a^2 - 36?

• (a + 6)(a + 6)

• (a - 6)(a - 6)

• (a + 6)(a - 6)

• (a - 6)(a + 12)

What should you do if you want to practice more problems on factoring polynomials?

• Ask a friend

• Watch the next video

• Ignore it

• Read a book