# Exploring the (a+b)^2 Equation

• Wardlaw
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.
Wardlaw
Math problem!

## Homework Statement

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

Wardlaw said:

## Homework Statement

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

## 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:

Wardlaw said:

## Homework Statement

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

## 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?

$$(a+b)^2$$
$$=(a+b)(a+b)$$
$$=a(a+b)+b(a+b)$$

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

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

Well this was weird.. xD

Is p+q+r=p+q+s never valid?

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

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

## 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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