Factoring: Difference of Squares

Factor the binomial, if possible:

x² - 25

• ( x + 5 ) ( x - 5 )

• ( x - 5 ) ( x - 5 )

• ( x + 5 ) ( x + 5 )

• This expression is unfactorable because 25 is not a perfect square.

Factor the expression, if possible:

x⁴ - 16

• ( 2x - 4)( 2x + 4)

• ( x² + 4)( x² - 4)

• ( x² - 8)( x² + 8)

• ( x - 4)( x + 4)

• Cannot be factored because x⁴ and 16 are not perfect squares.

Factor the following binomial:

x² - 225

• ( x + 25)( x + 25)

• Unfactorable because 225 is not a perfect square.

• ( x + 15)( x - 15)

• ( x - 15)( x - 15)

Which of the following choices are the factors for:

x⁶ - 400

• ( x³ - 200)(x³ + 200)

• ( x² + 20)(x² + 20)

• ( x - 20)(x + 20)

• ( x³ + 20)(x³ - 20)

Factor the binomial expression if possible:

9x² - 49y⁶

• ( 3x + 7y³) (3x + 7y³)

• ( 3x - 7y³) (3x + 7y³)

• ( 3x - 7y³) (3x - 7y³)

• Cannot be factored because they are not perfect squares.

Determine if the binomial below is factorable.

x² + 81

• Unfactorable because it does not have a subtraction symbol in the middle.

• ( x - 9 ) ( x + 9 )

• ( x + 9 ) ( x + 9 )

• ( x - 9 ) ( x - 9 )

Factor the binomial:

121r² - 64

• (11r + 8)(11r - 8)

• (11r - 8)(11r - 8)

• (11r + 8)(11r + 8)

• Unfactorable

Which of the following choices are the factors for:

25x² - 81

• (5x-9)²

• (5x+9)(5x-9)

• 25(x-9)²

• (9x+5)(9x-5)

Factor the following binomial:

4x² - 16

• (2x-4)(2x+4)

• (4x-4)(4x+4)

• 4(x-2)²

• 4(x-2)(x+2)

Factor the following binomial:

3x² - 75

• 3( x + 5 ) ( x - 5 )

• Cannot be factored because 3 is not a perfect square.

• ( x + 5 ) ( x - 5 )

• 3( x - 5 ) ( x - 5 )