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.

Examples 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(x2 + 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

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.]

Related Terms for Equivalent Expression

  • Algebraic expression
  • Expression
  • Variable