factorize each linear expression.\n1) 6x + 9\n2) -20y - 5z\n3) 15 - 3a\n4) 2m + 2\n5) 39u - 52v + 13\n6) 10z…

Explanation:

Step1: Find the greatest common factor (GCF)

For (6x + 9), the GCF of (6) and (9) is (3).

Step2: Factor out the GCF

(6x+9 = 3\times2x+3\times3=3(2x + 3))

Step1: Find the GCF

For (-20y-5z), the GCF of (20) and (5) is (5).

Step2: Factor out the GCF

(-20y - 5z=-5\times4y-5\times z=-5(4y + z))

Step1: Find the GCF

For (15-3a), the GCF of (15) and (3) is (3).

Step2: Factor out the GCF

(15-3a=3\times5-3\times a = 3(5 - a))

Step1: Find the GCF

For (2m + 2), the GCF of (2) and (2) is (2).

Step2: Factor out the GCF

(2m+2=2\times m+2\times1=2(m + 1))

Step1: Find the GCF

For (39u-52v + 13), the GCF of (39), (52) and (13) is (13).

Step2: Factor out the GCF

(39u-52v + 13=13\times3u-13\times4v+13\times1=13(3u-4v + 1))

Step1: Find the GCF

For (10z-60), the GCF of (10) and (60) is (10).

Step2: Factor out the GCF

(10z-60=10\times z-10\times6=10(z - 6))

Step1: Find the GCF

For (44p+11q), the GCF of (44) and (11) is (11).

Step2: Factor out the GCF

(44p+11q=11\times4p+11\times q=11(4p + q))

Step1: Find the GCF

For (42+35w), the GCF of (42) and (35) is (7).

Step2: Factor out the GCF

(42+35w=7\times6+7\times5w=7(6 + 5w))

Step1: Find the GCF

For (81n-36), the GCF of (81) and (36) is (9).

Step2: Factor out the GCF

(81n-36=9\times9n-9\times4=9(9n - 4))

Step1: Find the GCF

For (40b-80c-40d), the GCF of (40), (80) and (40) is (40).

Step2: Factor out the GCF

(40b-80c-40d=40\times b-40\times2c-40\times d=40(b - 2c - d))

Answer:

1. (3(2x + 3))
2. (-5(4y + z))
3. (3(5 - a))
4. (2(m + 1))
5. (13(3u-4v + 1))
6. (10(z - 6))
7. (11(4p + q))
8. (7(6 + 5w))
9. (9(9n - 4))
10. (40(b - 2c - d))