Foundations & Pre-Calculus 10 H
Worksheet (Factoring Special Polynomials)
YOU MUST SHOW YOUR WORK WHENEVER POSSIBLE!
1. Expand and simplify.
a)
x  2 2
b)
3  y 2
c)
5  d 5  d 
d)
7  f 7  f 
2. Identify each polynomial as a perfect square trinomial, a difference of squares or neither.
a) 25  t 2
b) 4 x 2  24 xy  9 y 2
c) 16m 2  49n 2
d) 9m 2  24mn  16n 2
3. Factor each polynomial.
a) x 2  49
b) 4 x 2  12 x  9
c) 9  30n  25n 2
d) b 2  121
e) 36  c 2
f) 81  36v  4v 2
g) 9d 2  16 f 2
h) 4 x 2  28xy  49 y 2
4. Factor completely. HINT: Determine the GCF first.
a) 8m 2  72n 2
b) 8 z 2  8 yz  2 y 2
c) 8 p 2  40 pq  50q 2
d) 128c 2  18b 2
5. Determine the area of the shaded region. Simplify your answer.
*6. Factor completely
a) (4𝑥 2 + 4𝑥𝑦 + 𝑦 2 ) − 9𝑧 2
b) 𝑥 8 − 1
c) 𝑥 6 − 4𝑥 3 𝑦 3 + 4𝑦 6
d) 42𝑚 𝑥 2𝑚 − 92𝑛 𝑦 2𝑛