Questions: Simplify the expression -5r + 4r/4 - 5s + 2rs given r=2, s=-4.

Solution Steps

To simplify the expression \(-5r + \frac{4r}{4} - 5s + 2rs\) given \(r=2\) and \(s=-4\), we can substitute the values of \(r\) and \(s\) into the expression and then perform the arithmetic operations.

Given the expression \(-5r + \frac{4r}{4} - 5s + 2rs\) and the values \(r = 2\) and \(s = -4\), we substitute these values into the expression:

\[ -5(2) + \frac{4(2)}{4} - 5(-4) + 2(2)(-4) \]

Simplify each term in the expression:

\[ -5(2) = -10 \]

\[ \frac{4(2)}{4} = 2 \]

\[ -5(-4) = 20 \]

\[ 2(2)(-4) = -16 \]

Combine the simplified terms to get the final result:

\[ -10 + 2 + 20 - 16 \]

Perform the arithmetic operations step-by-step:

\[ -10 + 2 = -8 \]

\[ -8 + 20 = 12 \]

\[ 12 - 16 = -4 \]

Final Answer