Jayden correctly simplifies the expression 9x(2+7x) using the following steps Step 1. 9(7x+2) Step 2. 9(7x) +9(2) Step 3. (9×7)x+18. What are the properties for each one?

Question

Jayden correctly simplifies the expression 9x(2+7x) using the following steps Step 1. 9(7x+2) Step 2. 9(7x) +9(2) Step 3. (9x7)x+18. What are the properties for each one?

Nick · Answer

How to solve:        Let's follow his process step-by-step to analyze what property is being used. The breakdown is as follows:    Process:   Jayden's work   Set up equation                                                     9(2 + 7x)  Step 1                                                                      9(7x + 2)  Step 2                                                                     9(7x) + 9(2)  Step 3                                                                      (9*7)x + 18     Breakdown   Set up equation                                                     9(2 + 7x)   Step 1: Commutative Property of Addition   This property states that  when adding, the order of the numbers being added does not matter, and are therefore interchangeable.    Original equation: 9(2 + 7x)  Equation's formula: a(b + c)  Changed equation: 9(7x + 2)  Equation's formula: a(c + b)  By swapping the b and c values in the parentheses, Jayden is demonstrating the Commutative Property. Both will still produce the same sum.        Step 2: Distributive Property of Multiplication   This property states that  the sum of two addends that are multiplied by the same number is equal to the product of that number multiplying the sum of both addends.   Original equation: 9(7x + 2)  Equation's formula: a(c + b)  Changed equation: 9(7x) + 9(2)  Equation's formula: a(c) + a(b)  By splitting the parentheses and multiplying each term separately, Jayden is demonstrating the Distributive Property. Both will produce the same product.        Step 3: Associative Property of Multiplication   This property states that  the product of three terms, where one is outside of the parentheses multiplying the other two, is not affected by changing which term is on the outside of the parentheses.   Original equation: 9(7 * x) +18  Equation's formula: a(c*x) + (ab)  Changed equation: x(7*9) + 18  Equation's forumula: x(c*a) +18  By swapping the 9 and x variables, Jayden is demonstrating the Associative Property. Both will produce the same product.       Simplified:   Step 1 - Commutative Property  Step 2 - Distributive Property  Step 3 - Associative Property

Process:

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