FACTORING SPECIAL PRODUCTS

 

Identify each of the following as either a difference of perfect squares, a sum of perfect squares, or a perfect square trinomial.  Then factor when possible.

 

1)      m2 – 25

 

2)      x2 + 16

 

3)      x2 – 16

 

4)      r2 – 2rs + s2

 

5)      25m2 – 16

 

6)      z2 – 14z + 49

 

7)      y2 – 9

 

8)      a2 – b2

 

9)      m2 + 100

 

10)  25a2 – 16r2

 

11)  k2 – 10k + 25

 

12)  m2 – 1

 

13)  a4 – 1

 

14)  m2 + 16m + 64

 

15)  p4 – 49

 

16)  q2 + p2

 

17)  36t2 – 16

 

18)  r4 – 9

 

19)  x4 + 4x2 + 4

 

20)  r8 – t8

 

21)  Identify the following type of special product and factor:  64x3 + 125y3

 

Answers:

 

 

 

1)      Difference of perfect squares:  (m – 5)(m + 5)

2)      Sum of perfect squares:  prime (not factorable)

3)      Difference of perfect squares:  (x – 4)(x + 4)

4)      Perfect square trinomial:  (r – s)(r – s) = (r – s)2

5)      Difference of perfect squares:  (5m – 4)(5m + 4)

6)      Perfect square trinomial:  (z – 7)(z – 7) = (z – 7)2

7)      Difference of perfect squares:  (y – 3)(y + 3)

8)      Difference of perfect squares:  (a – b)(a + b)

9)      Sum of perfect squares:  prime

10)  Difference of perfect squares:  (5a – 4r)(5a + 4r)

11)  Perfect square trinomial:  (k – 5)2

12)  Difference of perfect squares:  (m – 1)(m + 1)

13)  Difference of perfect squares:  (a2 – 1)(a2 + 1) = (a – 1)(a + 1)(a2 + 1)

14)  Perfect square trinomial:  (m + 8)2

15)  Difference of perfect squares:  (p2 – 7)(p2 + 7)

16)  Sum of perfect squares:  prime

17)  Difference of perfect squares with a greatest common factor of 4 that can be removed first:  4(9t2 – 4) = 4(3t – 2)(3t + 2)

18)  Difference of perfect squares:  (r2 – 3)(r2 + 3)

19)  Perfect square trinomial:  (x2 + 2)(x2 + 2)

20)  Difference of perfect squares:  (r4 – t4)(r4 + t4) = (r2 – t2)(r2 + t2)(r4 + t4) =

                                                        (r – t)(r + t)(r2 + t2)(r4 + t4)

21) Sum of perfect cubes:  (4x + 5y)(16x2 – 20xy + 25y2)