ALGEBRA I
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SECTION 8-2 : MULTIPLYING
and FACTORING
Simplify by distributing.
1) 3(2x + 5)
4) 2x(5x + 6)
ANSWER : 6x + 15
ANSWER : 10x2 + 12x
2) -5(4x – 3)
5) -y2(y + 6)
ANSWER : -20x + 15
ANSWER : -y3 – 6y2
3) 9(4x2 – 7)
6) 8w3 (4w2 + w – 8)
ANSWER : 36x2 - 63
ANSWER : 32w5 + 8w4 – 64w3
The Greatest Common Factor (GCF) is the largest
common term that is a factor of all of the original
terms.
Find the GCF. (Hint : do a prime factorization of each
term. The GCF is written using all common factors
along with their smallest exponents.)
7) 36 and 42
8) 24, 60, and 72
ANSWER : 6
ANSWER : 12
To find the GCF of two or more monomials, first find
the GCF of the “numbers”. For the variables, the GCF
includes all variables the monomials have in common
with their SMALLEST exponents.
9) 48ab2; 54a3bc
10)
60x3y4z5;
120x2y4z3
11) 21xy2; 25z
ANSWER : 6ab
ANSWER : 60x2y4z3
ANSWER : 1
Factor each polynomial.
12) 7x - 49
15) 12x2 – 3x
ANSWER : 7(x – 7)
ANSWER : 3x (4x – 1)
13) b2 – 14b
16) 80a4 + 60a3 – 50a2 + 10a
ANSWER : b(b – 14)
ANSWER : 10a(8a3 + 6a2 – 5a + 1)
14) 10x3 + 3x2
ANSWER : x2 (10x + 3)
Two Fathers and Two Sons Riddle. Two
fathers and two sons sat down to eat
eggs for breakfast. They ate exactly
three eggs, each person had an egg.
The riddle is for you to explain how.
One of the sons is
also a father.