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Difficulty: MediumSimplifying Algebraic Expressions

What is the result of fully expanding and simplifying the given algebraic expression?

−4k(2k−3m)+5k(k−2m)−3k2-4k(2k - 3m) + 5k(k - 2m) - 3k^2
  1. −6k2+2km-6k^2 + 2kmAnswer
  2. B
    −6k2−22km-6k^2 - 22km
  3. C
    −4k3m-4k^3m
  4. D
    −6k2−5m-6k^2 - 5m

Answer

The correct simplified expression is −6k2+2km-6k^2 + 2km.
The correct answer accurately expands the expression by distributing −4k-4k to get −8k2+12km-8k^2 + 12km, and 5k5k to get 5k2−10km5k^2 - 10km. Grouping the k2k^2 terms (−8+5−3=−6-8 + 5 - 3 = -6) and the kmkm terms (12−10=212 - 10 = 2) yields −6k2+2km-6k^2 + 2km.

Step-by-Step Solution

1
Distribute −4k-4k across the terms inside the first set of parentheses: (2k−3m)(2k - 3m).
−8k2+12km-8k^2 + 12km
To eliminate the first grouping symbol, being careful to multiply the negative signs properly (−4k×−3m=+12km-4k \times -3m = +12km).
2
Distribute 5k5k across the terms inside the second set of parentheses: (k−2m)(k - 2m).
5k2−10km5k^2 - 10km
To eliminate the second grouping symbol.
3
Write out the complete expanded expression by combining the results and the remaining −3k2-3k^2 term.
−8k2+12km+5k2−10km−3k2-8k^2 + 12km + 5k^2 - 10km - 3k^2
This shows all individual terms ready for grouping.
4
Identify and combine the like terms: the k2k^2 terms (−8k2-8k^2, 5k25k^2, −3k2-3k^2) and the kmkm terms (12km12km, −10km-10km).
−6k2+2km-6k^2 + 2km
Combining like coefficients (−8+5−3=−6-8 + 5 - 3 = -6 and 12−10=212 - 10 = 2) provides the final simplified expression in standard form.

Key Concept

Applying the distributive property with negative numbers and combining multivariable like terms.
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Topics

Simplifying Algebraic Expressions

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