Exploring the (a+b)^2 Equation

  • Thread starter Wardlaw
  • Start date
In summary, the answer is yes, (a+b)^2 is always equal to a^2+2ab+b^2 when a and b represent objects in a commutative ring like the real numbers. However, if multiplication is not commutative, (for example if a and b are matrices), then (a+b)^2 may not always equal a^2+2ab+b^2. Additionally, for numbers as they should be in high school, (a+b)^2 is always equal to a^2+2ab+b^2 and this holds true regardless of time or expiration dates. Furthermore, p+q+r will only be equal to p+q+s if r=s.
  • #1
Wardlaw
27
0
Math problem!

Homework Statement



Is (a+b)^2 ALWAYS equal to a^2+2ab+b^2?

Homework Equations





The Attempt at a Solution

 
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  • #2


Wardlaw said:

Homework Statement



Is (a+b)^2 ALWAYS equal to a^2+2ab+b^2?

Homework Equations


The Attempt at a Solution


Yes, if a and b represent objects in a commutative ring like the real numbers. If multiplication is not commutative, (for example a and b are matrices) then (a+b)^2=a^2+ab+ba+b^2 which is not generally the same. Why do you ask?
 
Last edited:
  • #3


Wardlaw said:

Homework Statement



Is (a+b)^2 ALWAYS equal to a^2+2ab+b^2?

Homework Equations





The Attempt at a Solution


If a and b are numbers as they should be if you're in high school, then yes, they're always equal. Why?

[tex](a+b)^2[/tex]
[tex]=(a+b)(a+b)[/tex]
[tex]=a(a+b)+b(a+b)[/tex]

And I'm sure you can expand out the rest.
 
  • #4


Math formulas generally don't have expiration or 'black out' dates.
 
  • #5


Well this was weird.. xD
 
  • #6


Is p+q+r=p+q+s never valid?
 
  • #7


Wardlaw said:
Is p+q+r=p+q+s never valid?

Only if r=s. Why do you want to know?
 

FAQ: Exploring the (a+b)^2 Equation

1. What is the (a+b)^2 equation?

The (a+b)^2 equation is a mathematical expression that represents the square of the sum of two numbers, a and b. It is written as (a+b)^2 = a^2 + 2ab + b^2.

2. How is the (a+b)^2 equation useful in science?

The (a+b)^2 equation is useful in science because it can be applied to various physical phenomena, such as calculating the area of a square, finding the force of an object, or analyzing the relationship between two variables.

3. What are the steps for solving the (a+b)^2 equation?

The steps for solving the (a+b)^2 equation are as follows:
1. Expand the equation by multiplying (a+b) by itself
2. Simplify the resulting expression
3. Combine like terms to get the final solution.

4. Can the (a+b)^2 equation be applied to more than two numbers?

Yes, the (a+b)^2 equation can be applied to any number of terms. For example, (a+b+c)^2 = a^2 + 2ab + 2ac + b^2 + 2bc + c^2.

5. How can the (a+b)^2 equation be used to understand patterns in nature?

The (a+b)^2 equation can be used to study patterns in nature by representing relationships between two variables. By plugging in different values for a and b, we can observe how the resulting expression changes and identify any patterns or trends. This can help us better understand and predict natural phenomena.

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