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Difficulty: EasyEvaluating Algebraic Expressions

If x=−2x = -2 and y=−3y = -3, what is the value of the expression 2x2−5y2x^2 - 5y?

  1. A
    -7
  2. B
    7
  3. 23Answer
  4. D
    31

Answer

23
The expression is evaluated by first substituting the values and applying the exponent to the base, giving (−2)2=4(-2)^2 = 4. Then, perform the multiplication to get 2(4)=82(4) = 8 and 5(−3)=−155(-3) = -15. Finally, subtracting negative 15 from 8 is the same as adding 15, resulting in 8+15=238 + 15 = 23.

Step-by-Step Solution

1
Substitute the given values for xx and yy into the expression.
2(−2)2−5(−3)2(-2)^2 - 5(-3)
To evaluate the expression, each variable must be replaced with its corresponding numerical value.
2
Evaluate the exponent.
2(4)−5(−3)2(4) - 5(-3)
According to the order of operations (PEMDAS), exponents must be resolved before multiplication. The square of any non-zero real number is positive, so (−2)2=4(-2)^2 = 4.
3
Perform the multiplication operations.
8−(−15)8 - (-15)
Multiply 22 by 44 to get 88, and 55 by −3-3 to get −15-15.
4
Perform the subtraction.
8+15=238 + 15 = 23
Subtracting a negative number is mathematically identical to adding its positive counterpart.

Key Concept

Evaluating expressions using substitution and the order of operations.
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Topics

Evaluating Algebraic Expressions

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