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Difficulty: EasySimplifying Algebraic Expressions

A student needs to simplify the expression 7k−2(k+4)+17k - 2(k + 4) + 1. What is the fully simplified form of this expression?

  1. 5k−75k - 7Answer
  2. B
    5k+95k + 9
  3. C
    5k+55k + 5
  4. D
    −2k-2k

Answer

The correct simplified expression is 5k−75k - 7.
The expression is simplified by first distributing the −2-2 into (k+4)(k + 4) to get −2k−8-2k - 8. Next, the like terms are combined: 7k−2k7k - 2k becomes 5k5k, and the constants −8-8 and 11 combine to −7-7. This results in the final simplified expression of 5k−75k - 7.

Step-by-Step Solution

1
Apply the distributive property to the term −2(k+4)-2(k + 4).
7k−2k−8+17k - 2k - 8 + 1
The multiplier −2-2 must be distributed to both kk and 44 inside the parentheses.
2
Group the like terms together.
(7k−2k)+(−8+1)(7k - 2k) + (-8 + 1)
Like terms (variables with the same exponent, and constants) are grouped so they can be combined.
3
Combine the grouped like terms to simplify the expression.
5k−75k - 7
Subtracting 2k2k from 7k7k gives 5k5k, and adding 11 to −8-8 gives −7-7.

Key Concept

Simplifying algebraic expressions by using the distributive property with negative multipliers and combining like terms.
Estimated Time:45s
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Topics

Simplifying Algebraic Expressions

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