Understanding the Difference of Two Squares

What is the result of multiplying (x + y) by (x - y)?

• x^2 + 2xy + y^2

• 2xy

• x^2 - y^2

• x^2 + y^2

Which of the following is the correct expression for the difference of two squares?

• x^2 + y^2 = (x + y)(x - y)

• x^2 - y^2 = (x - y)^2

• x^2 + y^2 = (x - y)^2

• x^2 - y^2 = (x + y)(x - y)

How can the expression x^2 - 9 be factored?

• (x + 9)(x - 9)

• (x + 3)(x + 3)

• (x + 3)(x - 3)

• (x + 1)(x - 9)

What is the factored form of a^2 - 4b^2?

• (a + b)(a - b)

• (a + 4b)(a - 4b)

• (a + 2b)^2

• (a + 2b)(a - 2b)

Which of the following expressions cannot be factored using the difference of two squares?

• x^2 + 25

• x^2 - 4

• x^2 - 16

• x^2 - 9

What is the greatest common factor of 24x^2 - 54?

• 12

• 2

• 6

• 3

How can x^4 - 16 be factored completely?

• (x^2 + 4)(x^2 - 4)

• (x^2 - 4)(x^2 + 4)

• (x^2 + 2)(x^2 - 2)

• (x^2 - 2)(x^2 + 2)

What is the factored form of 16x^8 - 81z^4?

• (4x^4 - 9z^2)(4x^4 + 9z^2)

• (4x^4 + 9z^2)(4x^4 - 9z^2)

• (2x^4 - 3z^2)(2x^4 + 3z^2)

• (2x^4 + 3z^2)(2x^4 - 3z^2)

Which expression represents a sum of two squares?

• x^2 - 9

• x^2 - 25

• x^2 - 16

• x^2 + 25

What is the result of factoring 64m^2 - 25n^2?

• (8m - 5n)(8m + 5n)

• (8m - 5n)^2

• (8m + 5n)^2

• (8m + 5n)(8m - 5n)