Answer:
-8x² + 28x - 20
Explanation:
To simplify the expression A(x) = ( 2x - 5 )( x + 1 ) - ( 5x - 3 )( 2x - 5 ), you can start by using the distributive property to expand both sets of parentheses and then combine like terms:
A ( x ) = ( 2x - 5 ) ( x + 1 ) - ( 5x - 3 ) ( 2x - 5 )
- Expand the first set of parentheses.
( 2x - 5 ) ( x + 1 )
2x ( x ) + 2x ( 1 ) - 5 ( x ) - 5 ( 1 )
2x² + 2x - 5x - 5
- Now, expand the second set of parentheses.
( 5x - 3 ) ( 2x - 5 )
5x ( 2x ) + 5x ( -5 ) - 3 ( 2x ) - 3 ( -5 )
10x² - 25x - 6x + 15
- Now, let's combine like terms within each part.
2x² + 2x - 5x - 5 - ( 10x² - 25x - 6x + 15)
- Distribute the negative sign to both terms in the second parentheses.
2x² + 2x - 5x - 5 - 10x² + 25x + 6x - 15
- Combine like terms in the entire expression.
( 2x² - 10x² ) + ( 2x - 5x + 25x + 6x ) + ( -5 - 15 )
-8x² + 28x - 20
∴ A ( x ) = -8x² + 28x - 20