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Zorluk: OrtaSimplifying Expressions and Combining Like Terms

For all real values of aa and bb, which of the following is equivalent to the expression 2a(a2−3b)−3(a3−2ab+b2)−(4b2−a3)2a(a^2 - 3b) - 3(a^3 - 2ab + b^2) - (4b^2 - a^3)?

  1. A
    −2a3−7b2-2a^3 - 7b^2
  2. B
    −12ab−7b2-12ab - 7b^2
  3. C
    −b2-b^2
  4. −7b2-7b^2Cevap
  5. E
    −2a3+2a2−7b2-2a^3 + 2a^2 - 7b^2

Cevap

−7b2-7b^2
Distributing the terms yields 2a3−6ab−3a3+6ab−3b2−4b2+a32a^3 - 6ab - 3a^3 + 6ab - 3b^2 - 4b^2 + a^3. Combining the like terms for a3a^3 gives 2a3−3a3+a3=02a^3 - 3a^3 + a^3 = 0. Combining the abab terms gives −6ab+6ab=0-6ab + 6ab = 0. Combining the b2b^2 terms gives −3b2−4b2=−7b2-3b^2 - 4b^2 = -7b^2. Thus, the simplified expression is −7b2-7b^2.

Adım Adım Çözüm

1
Distribute the factors outside the parentheses to each term inside the parentheses.
The terms expand to: 2a(a2)−2a(3b)−3(a3)−3(−2ab)−3(b2)−1(4b2)−1(−a3)=2a3−6ab−3a3+6ab−3b2−4b2+a32a(a^2) - 2a(3b) - 3(a^3) - 3(-2ab) - 3(b^2) - 1(4b^2) - 1(-a^3) = 2a^3 - 6ab - 3a^3 + 6ab - 3b^2 - 4b^2 + a^3
Distribution eliminates parentheses, making it possible to group and combine like terms.
2
Group like terms together based on their variable parts and powers.
(2a3−3a3+a3)+(−6ab+6ab)+(−3b2−4b2)(2a^3 - 3a^3 + a^3) + (-6ab + 6ab) + (-3b^2 - 4b^2)
Grouping like terms makes it easier to perform the arithmetic on the coefficients.
3
Combine the coefficients for each group of like terms.
0a3+0ab−7b2=−7b20a^3 + 0ab - 7b^2 = -7b^2
Simplifying the coefficient sums yields the final simplified form of the expression.

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Simplifying expressions by distributing terms and combining like terms
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Simplifying Expressions and Combining Like Terms

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