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Difficulty: MediumSimplifying Algebraic Expressions

Simplify the following algebraic expression:

8x−2[x−3(2x−y)]8x - 2[x - 3(2x - y)]

Which of the following represents the completely simplified form?

  1. A
    18x+2y18x + 2y
  2. B
    18x+6y18x + 6y
  3. 18x−6y18x - 6yAnswer
  4. D
    −30x2+18xy-30x^2 + 18xy

Answer

The completely simplified form is 18x−6y18x - 6y.
The expression is fully simplified by applying the distributive property iteratively, starting from the innermost parentheses, carefully tracking all negative signs, and finally combining like terms to arrive at 18x−6y18x - 6y.

Step-by-Step Solution

1
Distribute the -3 into the innermost parentheses.
−3(2x−y)=−6x+3y-3(2x - y) = -6x + 3y
According to the order of operations, innermost grouping symbols must be evaluated first. Distributing a negative number flips the signs of the terms inside.
2
Substitute this back and combine like terms inside the brackets.
x−6x+3y=−5x+3yx - 6x + 3y = -5x + 3y
Combining the like variable terms simplifies the expression inside the brackets before moving to the next operation.
3
Distribute the -2 across the newly simplified terms inside the bracket.
−2(−5x+3y)=10x−6y-2(-5x + 3y) = 10x - 6y
The distributive property applies the outside multiplier to every term within the brackets.
4
Combine this result with the remaining term outside the brackets.
8x+10x−6y=18x−6y8x + 10x - 6y = 18x - 6y
Adding the like x terms yields the final, completely simplified algebraic expression.

Key Concept

Simplifying Nested Algebraic Expressions
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Topics

Simplifying Algebraic Expressions

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