Algebra Demystified 2nd Ed

Chapter 6 FaCtoring and the distributive ProPerty 161

PRACTICE

Use the formula to factor the difference of two squares.

1. x^4 − 1 =


2. x^8 − 16 =


3. x^81
   16

–  = 

4. 256x^4 − 1 =


5. x^4 − 81 =


6. 81x^4 − 1 =
   7.^1
   64

x^6 –  =  1

8. 16x^4 − 81 =
   9.^16
   81

x^4 –  16 = 

10. x^12 − 1 =

✔SOLUTIONS

1. x^4 − 1 = (x^2 − 1)(x^2 + 1) = (x − 1)(x + 1)(x^2 + 1)


2. x^8 − 16 = (x^4 − 4)(x^4 + 4) = (x^2 − 2)(x^2 + 2)(x^4 + 4)


3. xx^841 xx^42
   16

1

4

1

4

1

2

–  =  –  +  =  – 







































xx^241

2

1

4

+  + 

4. 256x^4 − 1 = (16x^2 − 1)(16x^2 + 1) = (4x − 1)(4x + 1)(16x^2 + 1)


5. x^4 − 81 = (x^2 − 9)(x^2 + 9) = (x − 3)(x + 3)(x^2 + 9)


6. 81x^4 − 1 = (9x^2 − 1)(9x^2 + 1) = (3x − 1)(3x + 1)(9x^2 + 1)
   7.^1
   64

1 1

8

1 1

8

xx^63 –  =  –  x^3 +  1















8. 16x^4 − 81 = (4x^2 − 9)(4x^2 + 9) = (2x − 3)(2x + 3)(4x^2 + 9)
   9.^16
   81

16 4

9

4 4

9

xx^42 –  =  –  x^2 +  4















= ^2 –  +  + 

3

2 2

3

2 4

9

 xx x (^24)












10. x^12 − 1 = (x^6 − 1)(x^6 + 1) = (x^3 − 1)(x^3 + 1)(x^6 + 1)

PRACTICE

Use the formula to factor the difference of two squares.