Question

Difficulty: MediumOrder of Operations and Number Properties

If x=−3x = -3 and y=2y = 2, what is the value of the expression x2−y(x−y3)x^2 - y(x - y^3)?

  1. A
    -77
  2. B
    -1
  3. C
    13
  4. D
    27
  5. 31Answer

Answer

31
Substituting x=−3x = -3 and y=2y = 2 into the expression gives x2−y(x−y3)=(−3)2−2(−3−23)x^2 - y(x - y^3) = (-3)^2 - 2(-3 - 2^3). Evaluating exponents first, we get 9−2(−3−8)9 - 2(-3 - 8). Simplifying inside the parentheses gives 9−2(−11)9 - 2(-11). Multiplying before subtracting yields 9−(−22)=9+22=319 - (-22) = 9 + 22 = 31.

Step-by-Step Solution

1
Substitute the given values into the expression
(−3)2−2((−3)−23)(-3)^2 - 2((-3) - 2^3)
To evaluate the expression for the specific numbers x=−3x = -3 and y=2y = 2.
2
Evaluate the exponents outside and inside the parentheses
9−2(−3−8)9 - 2(-3 - 8)
Exponents must be calculated before multiplication and subtraction, according to PEMDAS rules. Note that (−3)2=9(-3)^2 = 9 and 23=82^3 = 8.
3
Perform the operations inside the parentheses
9−2(−11)9 - 2(-11)
Parentheses have the highest priority in the order of operations.
4
Multiply the terms
9−(−22)=9+229 - (-22) = 9 + 22
Multiplication must be performed before subtraction.
5
Perform final addition
31
Adding 22 to 9 yields the final simplified value.

Key Concept

Order of operations (PEMDAS) and substitution of negative numbers in exponents.
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