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Question

Difficulty: EasySimplifying Expressions and Combining Like Terms

For all real values of xx and yy, the expression 5x3y−2x2(3xy−y)−4x2y5x^3y - 2x^2(3xy - y) - 4x^2y can be simplified. Which of the following is equivalent to this simplified expression?

  1. A
    −x3y−6x2y-x^3y - 6x^2y
  2. B
    5x3y−8x2y5x^3y - 8x^2y
  3. −x3y−2x2y-x^3y - 2x^2yAnswer
  4. D
    −3x5y2-3x^5y^2
  5. E
    −x3y+6x2y-x^3y + 6x^2y

Answer

−x3y−2x2y-x^3y - 2x^2y
Distributing −2x2-2x^2 across the parentheses (3xy−y)(3xy - y) yields −6x3y+2x2y-6x^3y + 2x^2y. Substituting this back gives 5x3y−6x3y+2x2y−4x2y5x^3y - 6x^3y + 2x^2y - 4x^2y. Combining the x3yx^3y terms (5x3y−6x3y=−x3y5x^3y - 6x^3y = -x^3y) and the x2yx^2y terms (2x2y−4x2y=−2x2y2x^2y - 4x^2y = -2x^2y) yields the simplified expression −x3y−2x2y-x^3y - 2x^2y.

Step-by-Step Solution

1
Distribute the term −2x2-2x^2 to both terms inside the parentheses (3xy−y)(3xy - y).
−6x3y+2x2y-6x^3y + 2x^2y
Multiply −2x2-2x^2 by 3xy3xy (yielding −6x3y-6x^3y) and multiply −2x2-2x^2 by −y-y (yielding +2x2y+2x^2y).
2
Substitute the expanded terms back into the original expression.
5x3y−6x3y+2x2y−4x2y5x^3y - 6x^3y + 2x^2y - 4x^2y
Replace −2x2(3xy−y)-2x^2(3xy - y) with the expanded terms −6x3y+2x2y-6x^3y + 2x^2y.
3
Combine like terms by grouping the x3yx^3y terms and the x2yx^2y terms.
−x3y−2x2y-x^3y - 2x^2y
Combine 5x3y−6x3y=−x3y5x^3y - 6x^3y = -x^3y and 2x2y−4x2y=−2x2y2x^2y - 4x^2y = -2x^2y.

Key Concept

Simplifying expressions by distributing terms and combining like terms.
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Topics

Simplifying Expressions and Combining Like Terms

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