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Which pair of expressions below are equivalent?

r+r+r+r+s and 
5rs

4(8r) and 
12 r

4r+8s and 
8s+4r

9r+9r and 
81 r

Which pair of expressions below are equivalent?\newliner+r+r+r+s r+r+r+r+s and 5rs 5 r s \newline4(8r) 4(8 r) and 12r 12 r \newline4r+8s 4 r+8 s and 8s+4r 8 s+4 r \newline9r+9r 9 r+9 r and 81r 81 r

Full solution

Q. Which pair of expressions below are equivalent?\newliner+r+r+r+s r+r+r+r+s and 5rs 5 r s \newline4(8r) 4(8 r) and 12r 12 r \newline4r+8s 4 r+8 s and 8s+4r 8 s+4 r \newline9r+9r 9 r+9 r and 81r 81 r
  1. Compare Expressions: Compare the first pair of expressions.\newlineThe first expression is r+r+r+r+sr+r+r+r+s, which simplifies to 4r+s4r+s.\newlineThe second expression is 5rs5rs.\newlineThese two expressions are not equivalent because 4r+s4r+s does not equal 5rs5rs.
  2. Compare Expressions: Compare the second pair of expressions.\newlineThe first expression is 4(8r)4(8r), which simplifies to 32r32r.\newlineThe second expression is 12r12r.\newlineThese two expressions are not equivalent because 32r12r32r \neq 12r.
  3. Equivalent Expressions: Compare the third pair of expressions.\newlineThe first expression is 4r+8s4r+8s.\newlineThe second expression is 8s+4r8s+4r.\newlineThese two expressions are equivalent because addition is commutative, meaning that the order of the terms does not matter.
  4. Compare Expressions: Compare the fourth pair of expressions.\newlineThe first expression is 9r+9r9r+9r, which simplifies to 18r18r.\newlineThe second expression is 81r81r.\newlineThese two expressions are not equivalent because 18r18r does not equal 81r81r.

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