﻿ Definition and examples equivalent expressions | define equivalent expressions - Free Math Dictionary Online

# 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.

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.

### Solved Example on Equivalent Expression

• A. True
• B. False

#### 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

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