Problem 11 - Algebra and Trigonometry

Question

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

Step-by-Step Solution

Answer

Therefore, the value of the expression when \(x = 8\) and \(y = 2\) is \(46\).

Step 1: Subsituting Given Values

Start by substituting the given values into the expression. Replace \(x\) by 8 and \(y\) by 2 in the expression \(x^{2}-3(x-y)\), this makes our expression to look like this: \(8^{2}-3(8-2)\).

Step 2: Performing operations inside parentheses

According to the order of operations (PEMDAS/BODMAS), parentheses has the highest priority. Thus, Evaluate \(8-2\) inside the parentheses which results to \(8^{2}-3(6)\).

Step 3: Exponentiation

Next step is to find the square of 8 since exponentiation comes next in the order of operations. The expression then becomes \(64-3(6)\).

Step 4: Multiplication

Now, perform the multiplication operation which gives \(64-18\).

Step 5: Subtraction

Finally, perform the subtraction operation to find the computed value. This gives the result as \(46\).