Question

Complete the following equation:

(i) 28(100 + 2) = 2800 + _______
(ii) K(x + y) = _______ + _______
(iii) Using this idea find 18.

A) 200; Kxy; K + xy
B) 2800; Kx + Ky; Kxy
C) 2802; Kx + y; Kxy
D) 2828; K(x + y); K + x + y

Answer 1

The completed equations using the distributive property are 28(100 + 2) = 2800 + 56, and K(x + y) = Kx + Ky. For example, 18 multiplied by a sum of variables would use the distributive property similarly.

Step-by-step explanation:

The student has asked for help in completing the given equations. Here are the solutions:

1. 28(100 + 2) = 2800 + 56. Using the distributive property, 28 multiplied by 2 equals 56.
2. K(x + y) = Kx + Ky. Again, we apply the distributive property of multiplication over addition.
3. Referring to the idea in question (ii), when finding the value of 18 multiplied by the sum of some variables, akin to 'K' in the provided formula, the distributive property would apply similarly, resulting in 18 times each of the variables in the sum.

Therefore, solving these equations demonstrates the distributive property of multiplication over addition, which is a fundamental concept in mathematics and useful for simplifying equations and computations involving multiplication and even for factors related to variables.