Problem 12 - Algebra and Trigonometry

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

The evaluation of the given algebraic expression for the values \(x=8\) and \(y=3\) is \(44\).

Step 1: Substitute the Values

Replace the variables \(x\) and \(y\) in the given expression with the respective values. So, \(x^{2}-4(x-y)\) becomes \(8^{2}-4(8-3)\).

Step 2: Simplify Inside Parentheses

Perform the operation inside the parentheses first (according to the order of operations). This simplifies the expression to \(8^{2}-4(5)\).

Step 3: Compute the Exponential and Multiplication

Now, perform the operations of exponents and multiplication which will simplify the expression to \(64 - 4*5\).

Step 4: Final Simplification

Finally, perform the subtraction operation to get the final result. The expression simplifies to \(64 - 20\).