(2%2F5-x%2F2)-x%5E2%2B2x.jpeg "(x/2-2/5)(2/5-x/2)-x^2+2x")
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.