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Difficulty: HardProperties of Integers

If x=−3x = -3 and y=−5y = -5, what is the value of the following expression?

x2+2x×∣y∣−(x−y)x^2 + 2x \times |y| - (x - y)
  1. A
    -41
  2. -23Answer
  3. C
    13
  4. D
    37

Answer

The correct answer is -23.
By accurately applying the rules for negative integers, (-3)^2 evaluates to a positive 9. The absolute value |-5| evaluates to a positive 5. Following the order of operations, the multiplication 2(-3) * 5 is performed next, yielding -30. Finally, subtracting the evaluation of the parenthetical group (2) from the sum of 9 and -30 results in exactly -23.

Step-by-Step Solution

1
Substitute the values of x and y into the expression.
(−3)2+2(−3)×∣−5∣−(−3−(−5))(-3)^2 + 2(-3) \times |-5| - (-3 - (-5))
Direct substitution is the first step in evaluating algebraic expressions.
2
Evaluate the terms inside parentheses and absolute value brackets.
∣−5∣=5|-5| = 5 and (−3−(−5))=(−3+5)=2(-3 - (-5)) = (-3 + 5) = 2. The expression becomes: (−3)2+2(−3)×5−2(-3)^2 + 2(-3) \times 5 - 2
According to the order of operations, grouping symbols like absolute value and parentheses must be resolved first.
3
Evaluate the exponent.
(−3)2=9(-3)^2 = 9. The expression becomes: 9+2(−3)×5−29 + 2(-3) \times 5 - 2
Exponents must be calculated before multiplication, addition, and subtraction. A negative number squared yields a positive result.
4
Perform the multiplication.
2(−3)×5=−6×5=−302(-3) \times 5 = -6 \times 5 = -30. The expression becomes: 9+(−30)−29 + (-30) - 2
Multiplication is performed before addition and subtraction.
5
Perform the remaining addition and subtraction from left to right.
9−30−2=−21−2=−239 - 30 - 2 = -21 - 2 = -23
Addition and subtraction are the final steps in the order of operations.

Key Concept

Evaluating expressions using properties of negative integers and absolute value
Estimated Time:1m 0s
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Topics

Properties of Integers

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