Equivalent Expression

Definition of Equivalent Expression

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

More About Equivalent Expression

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

Video Examples:Solve Math Expressions Using The Order Of Operations


Example of Equivalent Expression

  • 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 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.

Solved Example on Equivalent Expression

Ques: 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.]