Understanding the Distributive Property: (n+1)^n(n+1)+1=n(n+1)^n+(n+1)^n+1

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In summary, the conversation discusses understanding the equation (n+1)^n(n+1)+1=n(n+1)^n+(n+1)^n+1 and how the first n on the RHS is related to a single addition of (n+1)^n. It is suggested to use the distributive property or the binomial theorem, and a hint is given to distribute the second term in parenthesis to the first term. This leads to the realization of the solution.
  • #1
Fabrizio
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Homework Statement


understanding the following equation:

##(n+1)^n(n+1)+1=n(n+1)^n+(n+1)^n+1##.

I don't know from where the first ##n## on the RHS comes and how this is related to a single addition of ##(n+1)^n##.

Homework Equations


##a(b+c)=ab+ac##

The Attempt at a Solution


My guess is that it has something to do with the distributive property or the binomial theorem, but i don't see how. The fact that this is very basic, i don't know how to attack the problem. I don't know of any intermediate steps. If someone wants to point out an intermediate step, it would be very much appreciated.
 
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  • #2
Hint: distribute the second term in parenthesis to the first term.
 
  • #3
Aaaah, now i see it. I can't believe i did not notice it earlier. Thanks for the hint!
 

Related to Understanding the Distributive Property: (n+1)^n(n+1)+1=n(n+1)^n+(n+1)^n+1

1. What is the Distributive Property?

The Distributive Property is a mathematical rule that states that when multiplying a number by a sum, you can distribute the multiplication to each addend and then add the products together. In other words, a(b+c) = ab + ac.

2. How do you apply the Distributive Property in equations?

To apply the Distributive Property in an equation, you must first identify a common factor between two or more terms. Then, you can distribute that factor to each term and combine like terms. For example, in the equation (n+1)^2, you can distribute the 2 to both the n and the 1, resulting in n^2 + 2n + 1.

3. What is the importance of the Distributive Property?

The Distributive Property is important in simplifying and solving equations, as well as in factoring and expanding expressions. It allows for easier manipulation of equations and makes solving for variables more efficient.

4. How does the Distributive Property apply to the equation (n+1)^n(n+1)+1=n(n+1)^n+(n+1)^n+1?

In this equation, we can first distribute the (n+1) to the (n+1)^n, resulting in (n+1)^(n+1). Then, we can distribute the (n+1) to the n, resulting in n^(n+1). Finally, we can combine like terms to get (n+1)^(n+1) + n^(n+1) + 1 = n^(n+1) + (n+1)^n + 1, which satisfies the Distributive Property.

5. Can the Distributive Property be applied to other operations besides multiplication?

Yes, the Distributive Property can also be applied to division, although it is less commonly used. For example, a/(b+c) = a/b + a/c. Additionally, it can be applied to exponents, such as (a+b)^2 = a^2 + 2ab + b^2.

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