Identifying equivalent algebraic expressions

Equivalent algebraic expressions are those expressions which on simplification give the same resulting expression.

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

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

Examples of Equivalent Expressions

3(x + 2) and 3x + 6 are equivalent expressions because the value of both the expressions remains the same for any value of x.

For instance, for x = 4,

3(x + 2) = 3(4 + 2) = 18 and

3x + 6 = 3 × 4 + 6 = 18.

The expressions 6(x² + 2y + 1) and 6x² + 12y + 6 are equivalent expressions

and can also be written as 6(x² + 2y + 1) = 6x² + 12y + 6.

In this lesson, we learn to identify equivalent expressions.

Given an expression, we select all equivalent expressions from a list.

For given expression, select one correct equivalent expression from the four options.

8y + 4y + 2y

A - 11y

B - y + 13

C - 7y - 6y

D - 9y + 5y

Solution

Step 1:

As 9y + 5y = 14y = 8y + 4y + 2y, the given expression

Step 2:

Only option D is the correct equivalent expression

For given expression, select one correct equivalent expression from the four options.

20x − 10y

A - 5(4x - 2y)

B - 10x + 25y

C - 5(5x + 2y)

D - 5(5x - 10y)

Solution

Step 1:

As 5(4x − 2y) = 20x − 10y, the given expression

Step 2:

Only option A is the correct equivalent expression

For given expression, select one correct equivalent expression from the four options.

15x + 25x²

A - 7(5x² + 2x)

B - 15x −35x²

C - 5x(3 + 5x)

D - 5(3 + 7x)

Solution

Step 1:

As 5x (3 + 5x) = 15x + 25x², the given expression

Step 2:

Only option C is the correct equivalent expression