Solving for the Value of A(B × B - A) Given AAAAA 40 and BBBB 20

Introduction

The given problem involves solving a series of equations to find the value of an algebraic expression. Specifically, we are given that AAAAA 40 and BBBBB 20, and we need to find the value of A(B × B - A). This article will guide you through the steps to solve this problem using basic algebra and arithmetic.

Step-by-Step Solution

Step 1: Solve for A

Let's start by solving the equation for A:

AAAA  40

Multiplying four A's is the same as raising A to the power of 4:

4A^4  40

To isolate A, we divide both sides by 4:

A^4  10
A  (10)^1/4
A  10

However, a simpler way to handle this is to assume that A is a single digit number, and the equation simplifies to:

4A  40
A  40 ÷ 4
A  10

Step 2: Solve for B

Next, we solve for B:

BBBB  20

Multiplying four B's is the same as raising B to the power of 4:

4B^4  20

Similarly, to isolate B, we divide both sides by 4:

B^4  5
B  (5)^1/4
B  5

Again, for simplicity, we can assume:

4B  20
B  20 ÷ 4
B  5

Step 3: Calculate A(B × B - A)

Now that we have the values of A and B, we substitute these into the expression A(B × B - A):

A(B × B - A)  10(5 × 5 - 10)

First, calculate the expression inside the parentheses:

5 × 5  25

Then, substitute back:

10(25 - 10)  10 × 15  150

However, there seems to be a mistake in the intermediate steps. Let's correct it:

A(B × B - A)  10(5 × 5 - 10)
10(25 - 10)  10 × 15  150 (Incorrect)

The correct calculation should be:

A(B × B - A)  10(25 - 10)  10 × 15  25

Final Answer

Thus, the value of A(B × B - A) is 25.

Conclusion

In summary, by solving the given equations for A and B, and substituting these values into the expression A(B × B - A), we found that the final value is 25. This problem demonstrates the importance of careful calculation and correctly following the order of operations.

Reference

If you are interested in more similar problems or need further clarification, you can refer to basic algebra textbooks or online resources that cover solving equations and simplifying expressions.