**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 3*x*+ 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 6*x*^{2}+ 6*y*+ 12 are equivalent expressions and can also be written as 6(*x*^{2}+*y*+ 2) = 6*x*^{2}+ 6*y*+ 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