## Simplifying the Expression (x/2-2/5)(2/5-x/2)-x^2+2x

This article will guide you through simplifying the algebraic expression **(x/2-2/5)(2/5-x/2)-x^2+2x**.

### Expanding the Expression

First, we need to expand the product of the two binomials:

(x/2 - 2/5)(2/5 - x/2) = (x/2)(2/5) + (x/2)(-x/2) + (-2/5)(2/5) + (-2/5)(-x/2)

Simplifying each term:

= x/5 - x^2/4 - 4/25 + x/5

Combining like terms:

= **2x/5 - x^2/4 - 4/25**

### Combining with the Remaining Terms

Now, we combine this simplified expression with the remaining terms:

2x/5 - x^2/4 - 4/25 - x^2 + 2x

Combining the x^2 terms:

= **-5/4x^2 + 2x/5 - 4/25 + 2x**

### Finding a Common Denominator

To further simplify, we can find a common denominator for the terms with x:

= -5/4x^2 + (4/4)(2x/5) - 4/25 + (20/20)(2x)

= -5/4x^2 + 8x/20 - 4/25 + 40x/20

= **-5/4x^2 + 48x/20 - 4/25**

### Simplified Expression

The simplified form of the original expression is **-5/4x^2 + 48x/20 - 4/25**.

You can further simplify by reducing the fraction 48/20, but the expression above is considered fully simplified.