1. ALGEBRA I - SECTION 8-2 (Multiplying and Factoring)
6/1/2019
ALGEBRA I @
SECTION 8-2 : MULTIPLYING and FACTORING

2. 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

3. 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

4. 9) 48ab2; 54a3bc 10) 60x3y4z5; 120x2y4z3 11) 21xy2; 25z
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
ANSWER : 6ab
10) 60x3y4z5; 120x2y4z3
ANSWER : 60x2y4z3
11) 21xy2; 25z
ANSWER : 1

5. 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)

6. One of the sons is also a father.
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.