Chapter 1 - Introduction to Algebraic Expressions - 1.2 The Commutative, Associative, and Distributive Laws - 1.2 Exercise Set - Page 18: 94

Associative law Distributive law The reverse of the Distributive law

The expression $(4\cdot3)a$ is changed to $4(3a)$. In Associative law, numbers can be grouped in any manner for multiplication. Since the brackets are shifted that means Associative law is used. The expression $4(b+5)$ is changed to $4(b)+4(5)$. In Distributive law, the product of a number and a sum can be written as the sum of the products. Since the product of $4$ and $(b+5)$ is converted to the sum of the products that means Distributive law is used. The expression $4(3a)+4(b)+4(5)$ is changed to $4(3a+b+5)$. In the reverse of the Distributive law, the sum of the products can be written as the product of a number and a sum. Since the sum of the products $4(3a)$, $4(b)$ and $4(5)$ is converted to the product of $4$ and $4(3a+b+5)$ that means reverse of the Distributive law is used.