Use the associative property of addition and the distributive property to justify that a(b+c+d) = ab +ac+ad
Help?
I don't know what it's asking..
The distributive property means you DISTRIBUTE a number/variable to other numbers in a set of parentheses. So, in this example, you would distribute a to b, c, and d to get this:
a => b
a => c
a => d
ab + ac + ad
But how do I justify my answer/use associative property?
Sure! The question is asking us to use the associative property of addition and the distributive property to prove that a multiplied by the sum of (b + c + d) is equal to the sum of (ab + ac + ad). Let's break it down step by step:
Step 1: Applying the associative property of addition
According to the associative property of addition, the grouping of numbers being added does not affect the sum. This means we can rearrange the terms within the parentheses without changing the value. So, we can rewrite (b + c + d) as (b + (c + d)).
Step 2: Applying the distributive property
The distributive property states that when we multiply a number by a sum of numbers, we can distribute the multiplication to each term inside the parentheses. In other words, a multiplied by (b + (c + d)) is equal to (a multiplied by b) plus (a multiplied by (c + d)).
Step 3: Simplifying the expression
Using the distributive property from Step 2, we have:
a(b + (c + d)) = ab + a(c + d)
Step 4: Applying the distributive property again
Now, we can distribute the multiplication of a to each term inside the parentheses (c + d):
ab + a(c + d) = ab + ac + ad
Step 5: Conclusion
Therefore, by applying the associative property of addition and the distributive property, we have proven that a multiplied by (b + c + d) equals (ab + ac + ad).
Hope this explanation helps! Let me know if you have any further questions.