What are the values of the following expression?
In each line, assume that:
x = 2.5 y = -1.5 m = 18 n = 4
x + n * y - (x + n) * y
To evaluate the expression ( x + n \cdot y - (x + n) \cdot y ) with the given values:
Let's break it down step by step.
Calculate ( n \cdot y ): [ n \cdot y = 4 \cdot (-1.5) = -6 ]
Calculate ( x + n ): [ x + n = 2.5 + 4 = 6.5 ]
Calculate ( (x + n) \cdot y ): [ (x + n) \cdot y = 6.5 \cdot (-1.5) = -9.75 ]
Now substitute these values back into the original expression: [ x + n \cdot y - (x + n) \cdot y = 2.5 + (-6) - (-9.75) ]
Simplify the expression: [ = 2.5 - 6 + 9.75 ] [ = 2.5 + 9.75 - 6 ] [ = 12.25 - 6 ] [ = 6.25 ]
Thus, the value of the expression ( x + n \cdot y - (x + n) \cdot y ) is ( \boxed{6.25} ).