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Difficulty: EasyEvaluating Algebraic Expressions

If x=−2x = -2 and y=3y = 3, what is the value of the algebraic expression 3x2−y2+4x3x^2 - y^2 + 4x?

  1. A
    −29-29
  2. −5-5Answer
  3. C
    1111
  4. D
    1313
  5. E
    1919

Answer

−5-5
Substituting x=−2x = -2 and y=3y = 3 gives 3(−2)2−(3)2+4(−2)3(-2)^2 - (3)^2 + 4(-2). Squaring −2-2 yields 44, so the first term becomes 3(4)=123(4) = 12. Squaring 33 yields 99, so the second term becomes −9-9. Multiplying 44 by −2-2 yields −8-8. Summing these values gives 12−9−8=−512 - 9 - 8 = -5.

Step-by-Step Solution

1
Substitute the given values x=−2x = -2 and y=3y = 3 into the expression 3x2−y2+4x3x^2 - y^2 + 4x.
3(−2)2−(3)2+4(−2)3(-2)^2 - (3)^2 + 4(-2)
Replace each variable with its respective numeric value.
2
Evaluate the exponential terms according to the order of operations (PEMDAS).
3(4)−9+4(−2)3(4) - 9 + 4(-2)
Squaring a negative number yields a positive result: (−2)2=4(-2)^2 = 4, and (3)2=9(3)^2 = 9.
3
Perform multiplication operations.
12−9−812 - 9 - 8
3⋅4=123 \cdot 4 = 12 and 4⋅(−2)=−84 \cdot (-2) = -8.
4
Add and subtract from left to right.
−5-5
12−9=312 - 9 = 3, and 3−8=−53 - 8 = -5.

Key Concept

Evaluating Algebraic Expressions with Signed Numbers
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Topics

Evaluating Algebraic Expressions

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