Difference of Two Squares

Question 1

What is the formula for the difference of two squares?

Answer 1

a² - b² = (a + b)(a - b)

Question 2

When can you apply the difference of two squares formula?

Answer 2

When you have an expression that is the subtraction of two perfect squares.

Question 3

What is a perfect square?

Answer 3

A perfect square is a number or term that can be written as something squared, like x², 9 (which is 3²), or 16y² (which is (4y)² ).

Question 4

Factor x² - 16 using the difference of two squares.

Answer 4

x² - 16 = (x+4)(x-4)

Question 5

Why does the difference of two squares formula work?

Answer 5

When you expand (a + b)(a - b), the middle terms cancel out, leaving a² - b²

Question 6

Factor 49y² - 36 using the difference of two squares.

Answer 6

49y² - 36 = (7y+6) (7y-6)

Question 7

True or False: You can use the difference of two squares formula on x² + 25 .

Answer 7

False, because the formula requires subtraction, not addition.

Question 8

How does factoring using the difference of two squares help in solving equations?

Answer 8

It simplifies the equation by breaking it into a product, making it easier to find the roots by setting each factor to zero.

Question 9

Factor 4x² - 81 .

Answer 9

4x² - 81 = (2x + 9)(2x - 9)

Question 10

Give an example of an expression that can be factored using the difference of two squares.

Answer 10

x² - 9,
25y² - 1,
100 - z²