Explanation of the expression AB square - BC square - AB C square:


Expression breakdown:

The given expression is AB square - BC square - AB C square.

Let's break down the expression and understand each term:

- AB square: This refers to the square of the length of line segment AB.
- BC square: This refers to the square of the length of line segment BC.
- AB C square: This refers to the square of the sum of the lengths of line segments AB and BC.

Calculation:

To solve this expression, we need to substitute the values of AB and BC with their respective lengths.

Let's assume that the length of AB is 'a' units and the length of BC is 'b' units.

The expression can now be written as:

(a^2) - (b^2) - (a + b)^2

To simplify further, we square the terms inside the brackets:

(a^2) - (b^2) - (a^2 + 2ab + b^2)

Now, let's simplify the expression by combining like terms:

a^2 - b^2 - a^2 - 2ab - b^2

The two terms a^2 and -a^2 cancel out, leaving us with:

-2ab - 2b^2

We can factor out a common factor of -2 from both terms:

-2(ab + b^2)

This is the simplified form of the given expression.

Conclusion:

The expression AB square - BC square - AB C square simplifies to -2(ab + b^2), where 'a' represents the length of line segment AB and 'b' represents the length of line segment BC. It is important to note that the final result is dependent on the values of 'a' and 'b'.