Questions: Evaluate the expression when x=5 and y=1 x(1+y)-3(x-y)=[?]

Transcript text: Simplifying and Evaluating Algebraic Expressions Evaluate the expression when \[ \begin{array}{c} x=5 \text { and } y=1 \\ x(1+y)-3(x-y)=[?] \end{array} \]

Solution

Solution Steps

To evaluate the given algebraic expression \( x(1+y)-3(x-y) \) when \( x=5 \) and \( y=1 \), substitute the values of \( x \) and \( y \) into the expression and perform the arithmetic operations.

Step 1: Substitute Values

We start by substituting the given values \( x = 5 \) and \( y = 1 \) into the expression \( x(1+y) - 3(x-y) \).

Step 2: Calculate Each Part

First, calculate \( 1 + y \): \[ 1 + y = 1 + 1 = 2 \] Next, calculate \( x(1+y) \): \[ x(1+y) = 5 \cdot 2 = 10 \] Now, calculate \( x - y \): \[ x - y = 5 - 1 = 4 \] Then, calculate \( 3(x-y) \): \[ 3(x-y) = 3 \cdot 4 = 12 \]

Step 3: Combine Results

Now, substitute these results back into the expression: \[ x(1+y) - 3(x-y) = 10 - 12 = -2 \]