Evaluate the expression below when [tex]x=-4[/tex].
[tex]4 x^2-2 x \times 15[/tex]
A. -56
B. 184
C. 376
D. 1,080

We need to evaluate the expression 4 x 2 − 2 x l ess im es 15 when x = − 4 .

Substitute x = − 4 into the expression: 4 l ess im es ( − 4 ) 2 − 2 l ess im es ( − 4 ) l ess im es 15 .
Simplify the exponent: ( − 4 ) 2 = 16 , so the expression becomes 4 l ess im es 16 − 2 l ess im es ( − 4 ) l ess im es 15 .
Perform the multiplications: 4 l ess im es 16 = 64 and − 2 l ess im es ( − 4 ) l ess im es 15 = 8 l ess im es 15 = 120 .
Subtract: 64 − ( − 120 ) = 64 + 120 = 184 . Therefore, the final answer is 184 ​ .

Explanation

Understanding the problem We are asked to evaluate the expression 4 x 2 − 2 x l ess im es 15 when x = − 4 . This means we need to substitute − 4 for x in the expression and simplify.

Substitution Substitute x = − 4 into the expression:


4 l ess im es ( − 4 ) 2 − 2 l ess im es ( − 4 ) l ess im es 15

Evaluating the exponent Now we simplify the expression using the order of operations (PEMDAS/BODMAS). First, we evaluate the exponent:

( − 4 ) 2 = ( − 4 ) l ess im es ( − 4 ) = 16
So the expression becomes:
4 l ess im es 16 − 2 l ess im es ( − 4 ) l ess im es 15

Multiplication Next, we perform the multiplications from left to right:

4 l ess im es 16 = 64
− 2 l ess im es ( − 4 ) = 8
So the expression becomes:
64 − ( 8 l ess im es 15 )

Multiplication Now we multiply 8 and 15 :

8 l ess im es 15 = 120
So the expression becomes:
64 − ( − 120 )

Subtraction Finally, we subtract − 120 from 64 :

64 − ( − 120 ) = 64 + 120 = 184
Examples
Evaluating algebraic expressions is a fundamental skill in mathematics with numerous real-world applications. For instance, consider a scenario where a company's profit, P , is modeled by the expression P = 4 x 2 − 2 x × 15 , where x represents the number of units sold. If the company sells x = − 4 units (perhaps due to returns or a specific accounting method), evaluating the expression helps determine the company's profit or loss. This skill is also essential in physics, engineering, and computer science for modeling and solving problems.

Answered by GinnyAnswer | 2025-07-03

By substituting x = − 4 into the expression 4 x 2 − 2 x × 15 and simplifying, we find that the result is − 56 . Therefore, the correct answer is option A. -56.
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Answered by Anonymous | 2025-07-04