Question

factor the expression using the gcf.

1. 9 + 21
2. 32 - 48
3. 8x + 2
4. 3y - 24
5. 20z - 8
6. 15w + 65
7. 36a + 16b
8. 21m - 49n

Explanation:

Problem 1: \(9 + 21\)

Step 1: Find GCF of 9 and 21

Factors of 9: \(1, 3, 9\); Factors of 21: \(1, 3, 7, 21\). GCF is \(3\).

Step 2: Factor out GCF

\(9 + 21 = 3\times3 + 3\times7 = 3(3 + 7)\)

Step 1: Find GCF of 32 and 48

Factors of 32: \(1, 2, 4, 8, 16, 32\); Factors of 48: \(1, 2, 3, 4, 6, 8, 12, 16, 24, 48\). GCF is \(16\).

Step 2: Factor out GCF

\(32 - 48 = 16\times2 - 16\times3 = 16(2 - 3)\)

Step 1: Find GCF of 8 and 2

Factors of 8: \(1, 2, 4, 8\); Factors of 2: \(1, 2\). GCF is \(2\).

Step 2: Factor out GCF

\(8x + 2 = 2\times4x + 2\times1 = 2(4x + 1)\)

Answer:

\(3(3 + 7)\)

Problem 2: \(32 - 48\)