Equivalent Expression

Definition of Equivalent Expressions

Two algebraic expressions are said to be equivalent if their values obtained by substituting the values of the variables are same.

More About Equivalent Expressions

To symbolize equivalent expressions an equality (=) sign is used.

Example of Equivalent Expressions

3(x + 3) and 3x + 9 are equivalent expressions, because the value of both the expressions remains same for any value of x. For instance, for x = 4, 3(x + 3) = 3(4 + 3) = 21 and 3(x + 9) = 3 x 4 + 9( x + 3) = 21.
The expressions 6(x 2 + y + 2) and 6x2 + 6y + 12 are equivalent expressions and can also be written as 6(x2 + y + 2) = 6x2 + 6y + 12.


Video Examples:Solve Math Expressions Using The Order Of Operations


Solved Example on Equivalent Expression

Expressions 3x2 – 6x + 3 and 3(x2 – 2x +1) are equivalent. Say true or false

Choices:
  • A. True
  • B. False

Correct Answer: A

Solution:

  • Step 1: 3x2 – 6x + 3 and 3(x2 – 2x +1) [Given expressions]
  • Step 2: Substitute x = 2 in both expressions
  • Step 3: First equation: 3(2)2 – 6(2) + 3 = 12 – 12 + 3 = 3 [Substitute and simplify]
  • Step 4: Second Equation: 3((2)2 – 2(2) + 1) = 3(4 – 4 + 1) = 3(1) = 3 [Substitute and simplify]
  • Step5: So, the two expressions, 3x2 – 6x + 3 and 3(x2 – 2x +1) are equivalent

Choose an expression that is equivalent to the expression 2n + 7(3 + n)

Choices:
  • A. 9n + 21
  • B. -9n + 21
  • C. -9n – 21
  • D. n + 21

Correct Answer: A

Solution:

  • Step 1: 2n + 7(3 + n) [Original expression]
  • Step 2: = 2n + 7(3) + 7(n) [Use the distributive property]
  • Step 3: = 2n + 21 + 7n [Multiply]
  • Step 4: = 2n + 7n + 21 [Use the commutative property]
  • Step 5: = 9n + 21 [Combine like terms]
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