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- Combining like terms: Whole number coefficients
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- Multiplying a constant and a linear monomial
- Distributive property: Whole Number coefficients
- Factoring a linear binomial
- Identifying parts in an algebraic expression
- Identifying equivalent algebraic expressions
- Introduction to properties of multiplication

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# 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(x^{2} + 2y + 1) and 6x^{2} + 12y + 6 are equivalent expressions

and can also be written as 6(x^{2} + 2y + 1) = 6x^{2} + 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 + 25x^{2}

**A** - 7(5x^{2} + 2x)

**B** - 15x −35x^{2}

**C** - 5x(3 + 5x)

**D** - 5(3 + 7x)

### Solution

**Step 1:**

As 5x (3 + 5x) = 15x + 25x^{2}, the given expression

**Step 2:**

Only option **C** is the correct equivalent expression