Problem 12 - College Algebra Essentials

Question

Evaluate each algebraic expression for the given value or values of the variable(s). $$x^{2}-4(x-y), \text { for } x=8 \text { and } y=3$$

Step-by-Step Solution

Answer

When \(x = 8\) and \(y = 3\), the expression \(x^{2}-4(x-y)\) evaluates to \(44\).

Step 1: Substitute given values

Substitute the given values \(x=8\) and \(y=3\) into the algebraic expression: \(8^{2}-4(8-3)\).

Step 2: Evaluate inside the parentheses

According to the rule of operations (PEMDAS/BODMAS), perform the operations inside the parentheses first: \(8^{2}-4(5)\).

Step 3: Perform exponentiation

First, calculate the exponentiation: \(64 - 4(5)\).

Step 4: Perform the multiplication

Next, perform the multiplication: \(64 - 20\).

Step 5: Perform the subtraction

Lastly, perform the subtraction: \(44\).