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Chapter 0: Problem 12

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

Short Answer

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

Step by step solution

01

Substitute the Values

Replace the variables \(x\) and \(y\) in the given expression with the respective values. So, \(x^{2}-4(x-y)\) becomes \(8^{2}-4(8-3)\).
02

Simplify Inside Parentheses

Perform the operation inside the parentheses first (according to the order of operations). This simplifies the expression to \(8^{2}-4(5)\).
03

Compute the Exponential and Multiplication

Now, perform the operations of exponents and multiplication which will simplify the expression to \(64 - 4*5\).
04

Final Simplification

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

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Most popular questions from this chapter

Determine whether each statement makes sense or does not make sense, and explain your reasoning. I simplified the terms of \(2 \sqrt{20}+4 \sqrt{75},\) and then I was able to add the like radicals.

Factor completely. $$2 x^{2}-7 x y^{2}+3 y^{4}$$

Exercises \(142-144\) will help you prepare for the material covered in the next section. Simplify and express the answer in descending powers of \(x\) : $$2 x\left(x^{2}+4 x+5\right)+3\left(x^{2}+4 x+5\right)$$

Factor and simplify each algebraic expression. $$-8(4 x+3)^{-2}+10(5 x+1)(4 x+3)^{-1}$$

will help you prepare for the material covered in the first section of the next chapter. If \(y=4-x^{2},\) find the value of \(y\) that corresponds to values of \(x\) for each integer starting with \(-3\) and ending with 3 .
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