Question

factoring / distributive property worksheet
factor the expressions.
1 a. 108 + 84z \t\t1 b. 44 + 20r
2 a. 84t + 77 \t\t2 b. 108 + 63b
3 a. 8 + 12n \t\t3 b. 77 + 42y
4 a. 56t + 40 \t\t4 b. 55w + 25
5 a. 48 + 54n \t\t5 b. 121z + 88
6 a. 121c + 99 \t\t6 b. 55u + 35
7 a. 49 + 70r \t\t7 b. 22z + 14

Explanation:

Let's solve 1a: \(108 + 84z\)

Step1: Find GCF of 108 and 84

Factors of 108: \(1, 2, 3, 4, 6, 9, 12, 18, 27, 36, 54, 108\)
Factors of 84: \(1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, 84\)
GCF is 12.

Step2: Factor out GCF

\(108 + 84z = 12\times9 + 12\times7z = 12(9 + 7z)\)

Now 1b: \(44 + 20r\)

Step1: Find GCF of 44 and 20

Factors of 44: \(1, 2, 4, 11, 22, 44\)
Factors of 20: \(1, 2, 4, 5, 10, 20\)
GCF is 4.

Step2: Factor out GCF

\(44 + 20r = 4\times11 + 4\times5r = 4(11 + 5r)\)

2a: \(84t + 77\)

Step1: Find GCF of 84 and 77

Factors of 84: \(1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, 84\)
Factors of 77: \(1, 7, 11, 77\)
GCF is 7.

Step2: Factor out GCF

\(84t + 77 = 7\times12t + 7\times11 = 7(12t + 11)\)

2b: \(108 + 63b\)

Step1: Find GCF of 108 and 63

Factors of 108: \(1, 2, 3, 4, 6, 9, 12, 18, 27, 36, 54, 108\)
Factors of 63: \(1, 3, 7, 9, 21, 63\)
GCF is 9.

Step2: Factor out GCF

\(108 + 63b = 9\times12 + 9\times7b = 9(12 + 7b)\)

3a: \(8 + 12n\)

Step1: Find GCF of 8 and 12

Factors of 8: \(1, 2, 4, 8\)
Factors of 12: \(1, 2, 3, 4, 6, 12\)
GCF is 4.

Step2: Factor out GCF

\(8 + 12n = 4\times2 + 4\times3n = 4(2 + 3n)\)

3b: \(77 + 42y\)

Step1: Find GCF of 77 and 42

Factors of 77: \(1, 7, 11, 77\)
Factors of 42: \(1, 2, 3, 6, 7, 14, 21, 42\)
GCF is 7.

Step2: Factor out GCF

\(77 + 42y = 7\times11 + 7\times6y = 7(11 + 6y)\)

4a: \(56t + 40\)

Step1: Find GCF of 56 and 40

Factors of 56: \(1, 2, 4, 7, 8, 14, 28, 56\)
Factors of 40: \(1, 2, 4, 5, 8, 10, 20, 40\)
GCF is 8.

Step2: Factor out GCF

\(56t + 40 = 8\times7t + 8\times5 = 8(7t + 5)\)

4b: \(55w + 25\)

Step1: Find GCF of 55 and 25

Factors of 55: \(1, 5, 11, 55\)
Factors of 25: \(1, 5, 25\)
GCF is 5.

Step2: Factor out GCF

\(55w + 25 = 5\times11w + 5\times5 = 5(11w + 5)\)

5a: \(48 + 54n\)

Step1: Find GCF of 48 and 54

Factors of 48: \(1, 2, 3, 4, 6, 8, 12, 16, 24, 48\)
Factors of 54: \(1, 2, 3, 6, 9, 18, 27, 54\)
GCF is 6.

Step2: Factor out GCF

\(48 + 54n = 6\times8 + 6\times9n = 6(8 + 9n)\)

5b: \(121z + 88\)

Step1: Find GCF of 121 and 88

Factors of 121: \(1, 11, 121\)
Factors of 88: \(1, 2, 4, 8, 11, 22, 44, 88\)
GCF is 11.

Step2: Factor out GCF

\(121z + 88 = 11\times11z + 11\times8 = 11(11z + 8)\)

6a: \(121c + 99\)

Step1: Find GCF of 121 and 99

Factors of 121: \(1, 11, 121\)
Factors of 99: \(1, 3, 9, 11, 33, 99\)
GCF is 11.

Step2: Factor out GCF

\(121c + 99 = 11\times11c + 11\times9 = 11(11c + 9)\)

6b: \(55u + 35\)

Step1: Find GCF of 55 and 35

Factors of 55: \(1, 5, 11, 55\)
Factors of 35: \(1, 5, 7, 35\)
GCF is 5.

Step2: Factor out GCF

\(55u + 35 = 5\times11u + 5\times7 = 5(11u + 7)\)

7a: \(49 + 70r\)

Step1: Find GCF of 49 and 70

Factors of 49: \(1, 7, 49\)
Factors of 70: \(1, 2, 5, 7, 10, 14, 35, 70\)
GCF is 7.

Step2: Factor out GCF

\(49 + 70r = 7\times7 + 7\times10r = 7(7 + 10r)\)

7b: \(22z + 14\)

Step1: Find GCF of 22 and 14

Factors of 22: \(1, 2, 11, 22\)
Factors of 14: \(1, 2, 7, 14\)
GCF is 2.

Step2: Factor out GCF

\(22z + 14 = 2\times11z + 2\times7 = 2(11z + 7)\)

Answer:

1a: \(12(9 + 7z)\)
1b: \(4(11 + 5r)\)
2a: \(7(12t + 11)\)
2b: \(9(12 + 7b)\)
3a: \(4(2 + 3n)\)
3b: \(7(11 + 6y)\)
4a: \(8(7t + 5)\)
4b: \(5(11w + 5)\)
5a: \(6(8 + 9n)\)
5b: \(11(11z + 8)\)
6a: \(11(11c + 9)\)
6b: \(5(11u + 7)\)
7a: \(7(7 + 10r)\)
7b: \(2(11z + 7)\)