Question

32
study the equation below.
$2k \times (5 + 6k) = (2k \times 5) + (2k \times 6k)$
which property of operation does the equation show?
a. associative property
b. commutative property
c. distributive property
d. identity property

Explanation:

Step1: Recall distributive property

The distributive property states that $a \times (b + c) = (a \times b) + (a \times c)$

Step2: Match to given equation

In $2k \times (5 + 6k) = (2k \times 5) + (2k \times 6k)$, set $a=2k$, $b=5$, $c=6k$. This matches the distributive property form exactly.

Step3: Eliminate other properties

• Associative: $(a \times b) \times c = a \times (b \times c)$ (not matching)
• Commutative: $a \times b = b \times a$ (not matching)
• Identity: $a \times 1 = a$ (not matching)

Answer:

C. Distributive property