Question

b. $9^0 = 9$
c. $7^2 = 7 \times 7$

1. find the gcf for each pair of numbers. then, use the gcf and the distributive property to find the sum of each pair of numbers.

a. 25 and 50
b. 7 and 49

Explanation:

Part a: 25 and 50

Step 1: Find GCF of 25 and 50

Factors of 25: \(1, 5, 25\)
Factors of 50: \(1, 2, 5, 10, 25, 50\)
GCF is \(25\).

Step 2: Use Distributive Property

Rewrite \(25 + 50\) as \(25 \times 1 + 25 \times 2\).
By distributive property \(a(b + c)=ab + ac\), reverse it: \(ab + ac = a(b + c)\).
So, \(25(1 + 2)=25 \times 3 = 75\).

Part b: 7 and 49

Step 1: Find GCF of 7 and 49

Factors of 7: \(1, 7\)
Factors of 49: \(1, 7, 49\)
GCF is \(7\).

Step 2: Use Distributive Property

Rewrite \(7 + 49\) as \(7 \times 1 + 7 \times 7\).
By distributive property, \(7(1 + 7)=7 \times 8 = 56\).

Answer:

s:
a. GCF = 25, Sum = \(25 + 50 = 75\) (or \(25(1 + 2)=75\))
b. GCF = 7, Sum = \(7 + 49 = 56\) (or \(7(1 + 7)=56\))