Understanding the Difference of Squares

The video tutorial explains the concept of binomials with opposite signs, focusing on the difference of squares. It demonstrates how terms cancel each other out, resulting in a binomial answer. Examples using (2z - 5)(2z + 5) and (4r + 7y)(4r - 7y) illustrate the process. The tutorial emphasizes the importance of sign and order in multiplication, showing that the order of factors does not affect the product.

What happens to the middle terms when you apply the FOIL method to (x + 4)(x - 4)?

• They add up to a positive number.

• They cancel each other out.

• They remain unchanged.

• They multiply to form a new term.

What is the result of simplifying (x + 4)(x - 4) using the difference of squares?

• x^2 - 16

• x^2 + 16

• x^2 - 8x + 16

• x^2 + 8x + 16

In the expression (2z - 5)(2z + 5), what is the product of the outer and inner terms?

• 4z^2 and -25

• 2z and -2z

• 10z and -10z

• 5z and -5z

What is the final result of (2z - 5)(2z + 5) when simplified?

• 4z^2 + 10z - 25

• 4z^2 - 10z + 25

• 4z^2 - 25

• 4z^2 + 25

Why does the order of multiplication not matter in expressions like (4r + 7y)(4r - 7y)?

• Because the terms are constants.

• Because of the commutative property.

• Because the terms are identical.

• Because of the associative property.

What is the simplified form of (4r + 7y)(4r - 7y)?

• 16r^2 - 14ry + 49y^2

• 16r^2 + 14ry - 49y^2

• 16r^2 - 49y^2

• 16r^2 + 49y^2