## Related Words

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

### Video Examples:Solve Math Expressions Using The Order Of Operations

### Solved Example on Equivalent Expression

#### Expressions 3x^{2} – 6x + 3 and 3(x^{2} – 2x +1) are equivalent. Say true or false

##### Choices:

- A. True
- B. False

Correct Answer: A

#### Solution:

- Step 1: 3x
^{2}– 6x + 3 and 3(x^{2}– 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, 3x
^{2}– 6x + 3 and 3(x^{2}– 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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