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Difficulty: MediumSimplifying Algebraic Expressions

What is the completely simplified form of the algebraic expression 7x−4(2x−3y)+5y7x - 4(2x - 3y) + 5y?

  1. A
    −x−7y-x - 7y
  2. B
    −x+2y-x + 2y
  3. −x+17y-x + 17yAnswer
  4. D
    7x+4xy+5y7x + 4xy + 5y

Answer

−x+17y-x + 17y
To completely simplify the expression, you must first distribute the −4-4 across the terms in the parentheses. Multiplying −4-4 by 2x2x gives −8x-8x, and multiplying −4-4 by −3y-3y gives +12y+12y (since a negative times a negative is a positive). Substituting this back gives 7x−8x+12y+5y7x - 8x + 12y + 5y. Finally, group the like variables: 7x−8x=−x7x - 8x = -x, and 12y+5y=17y12y + 5y = 17y. Combining these gives −x+17y-x + 17y.

Step-by-Step Solution

1
Distribute the −4-4 to both terms inside the parentheses (2x−3y)(2x - 3y).
−8x+12y-8x + 12y
The distributive property must be applied first to eliminate the parentheses, paying careful attention to the multiplication of two negative numbers (−4-4 and −3y-3y).
2
Rewrite the full expression incorporating the expanded terms.
7x−8x+12y+5y7x - 8x + 12y + 5y
This sets up the expression so that all individual terms are clearly visible for grouping.
3
Combine the like terms for both xx and yy.
−x+17y-x + 17y
Adding the coefficients of identical variables (7x−8x=−x7x - 8x = -x and 12y+5y=17y12y + 5y = 17y) provides the expression in its final standard form.

Key Concept

Simplifying Algebraic Expressions via Distributive Property and Like Terms
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Topics

Simplifying Algebraic Expressions

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