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Question

Difficulty: EasySimplifying Expressions and Combining Like Terms

Match each algebraic expression on the left with its fully simplified equivalent expression on the right.

  • −−(a2−2ab)+a(a−3b)--(a^2 - 2ab) + a(a - 3b)−ab-ab
  • 2(a2b−ab)−ab(2a−3)2(a^2b - ab) - ab(2a - 3)abab
  • a2(a−b)−a(a2−ab)a^2(a - b) - a(a^2 - ab)00

Answer

The expression −−(a2−2ab)+a(a−3b)--(a^2 - 2ab) + a(a - 3b) simplifies to −ab-ab; the expression 2(a2b−ab)−ab(2a−3)2(a^2b - ab) - ab(2a - 3) simplifies to abab; and the expression a2(a−b)−a(a2−ab)a^2(a - b) - a(a^2 - ab) simplifies to 00.
Each expression is correctly simplified by distributing the external factors across parenthetical terms and combining the resulting like terms.

Step-by-Step Solution

1
Simplify the first expression by distributing coefficients and combining like terms.
−−a2+2ab+a2−3b=−ab--a^2 + 2ab + a^2 - 3b = -ab
Distributing the negative sign yields −−a2+2ab--a^2 + 2ab and distributing aa yields a2−3aba^2 - 3ab. Adding them eliminates the a2a^2 terms, leaving −ab-ab.
2
Simplify the second expression by distributing coefficients and combining like terms.
2a2b−2ab−2a2b+3ab=ab2a^2b - 2ab - 2a^2b + 3ab = ab
Distributing 22 yields 2a2b−2ab2a^2b - 2ab and distributing −ab-ab yields −2a2b+3ab-2a^2b + 3ab. Adding them eliminates the 2a2b2a^2b terms, leaving abab.
3
Simplify the third expression by distributing coefficients and combining like terms.
a3−a2b−a3+a2b=0a^3 - a^2b - a^3 + a^2b = 0
Distributing a2a^2 yields a3−a2ba^3 - a^2b and distributing −a-a yields −a3+a2b-a^3 + a^2b. Adding them eliminates all terms, leaving 00.

Key Concept

Simplifying algebraic expressions containing multiple variables and higher powers by applying the distributive property and combining like terms.
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Topics

Simplifying Expressions and Combining Like Terms

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