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)