Question

1. write each of the following binomials as the product of its gcf with another binomial.

(a) $8x + 24$
(b) $10w - 5$
(c) $2n + 16$
(d) $6y + 21$
(e) $44x + 55$
(f) $28e - 7$
(g) $6x + 42y$
(h) $18m - 45n$
(i) $20c - 8d$

Explanation:

Step1: Find GCF of terms

(a) GCF of 8x,24 is 8

$\gcd(8,24)=8$

(b) GCF of 10w,5 is 5

$\gcd(10,5)=5$

(c) GCF of 2n,16 is 2

$\gcd(2,16)=2$

(d) GCF of 6y,21 is 3

$\gcd(6,21)=3$

(e) GCF of 44x,55 is 11

$\gcd(44,55)=11$

(f) GCF of 28e,7 is 7

$\gcd(28,7)=7$

(g) GCF of 6x,42y is 6

$\gcd(6,42)=6$

(h) GCF of 18m,45n is 9

$\gcd(18,45)=9$

(i) GCF of 20c,8d is 4

$\gcd(20,8)=4$

Step2: Factor out GCF from binomial

(a) Divide each term by 8

$8x+24=8(x+3)$

(b) Divide each term by 5

$10w-5=5(2w-1)$

(c) Divide each term by 2

$2n+16=2(n+8)$

(d) Divide each term by 3

$6y+21=3(2y+7)$

(e) Divide each term by 11

$44x+55=11(4x+5)$

(f) Divide each term by 7

$28e-7=7(4e-1)$

(g) Divide each term by 6

$6x+42y=6(x+7y)$

(h) Divide each term by 9

$18m-45n=9(2m-5n)$

(i) Divide each term by 4

$20c-8d=4(5c-2d)$

Answer:

(a) $8(x+3)$
(b) $5(2w-1)$
(c) $2(n+8)$
(d) $3(2y+7)$
(e) $11(4x+5)$
(f) $7(4e-1)$
(g) $6(x+7y)$
(h) $9(2m-5n)$
(i) $4(5c-2d)$