**Generating equivalent expressions worksheet :**

Worksheet on generating equivalent expressions is much useful to the students who would like to practice problems on "Equivalent algebraic expressions"

1. Simplify the expression 6x² - 4x²

2. Simplify the expression 3a + 2(b + 5a)

3. Simplify the expression y + 11x + 7y - 7x

4. Simplify the expression 8m + 14 - 12 + 4n

5. Simplify the expression 6x² + 4(x² - 1)

**Problem 1 : **

Simplify the expression 6x² - 4x²

**Solution :**

In the given expression, 6x² and 4x² are like terms.

Use the distributive property for like terms

6x² - 4x² = x²(6 - 4)

Subtract inside the parentheses.

6x² - 4x² = x²(2)

Use commutative property of multiplication

6x² - 4x² = 2x²

Hence, the expression equivalent to 6x² - 4x² is** 2x****²**

**Problem 2 : **

Simplify the expression 3a + 2(b + 5a)

**Solution :**

Use distributive property in 2(b + 5a)

3a + 2(b + 5a) = 3a + 2b + 2(5a)

Use the associative property of multiplication in 2(5a)

3a + 2(b + 5a) = 3a + 2b + (5·2)a

Multiply 2 and 5 in (5·2)a

3a + 2(b + 5a) = 3a + 2b + 10a

3a + 2(b + 5a) = 3a + 10a + 2b

Use the distributive property in 3a + 10a

3a + 2(b + 5a) = (3 + 10)a + 2b

Add inside the parentheses

3a + 2(b + 5a) = 13a + 2b

Hence, the expression equivalent to 3a+2(b+5a) is** 13a+2b**

**Problem 3 : **

Simplify the expression y + 11x + 7y - 7x

**Solution :**

In the given expression, 11x & 7x are like terms and y & 7y are like terms.

Use commutative property of addition in 11x + 7y

y + 11x + 7y - 7x = y + 7y + 11x - 7x

Use distributive property in y + 7y and 11x - 7x

y + 11x + 7y - 7x = (1 + 7)y + (11 - 7)x

Perform operations inside parentheses.

y + 11x + 7y - 7x = 8y + 4x

Use commutative property of addition in 8y + 4x

y + 11x + 7y - 7x = 4x + 8y

Hence, the expression equivalent to y + 11x + 7y - 7x is** 4x+8y**

**Problem 4 : **

Simplify the expression 8m + 14 - 12 + 4n

**Solution :**

In the given expression, 14 and 12 are like terms.

Combine the like terms 14 and 12 by subtracting 12 from 14

8m + 14 - 12 + 4n = 8m + 2 + 4n

Use commutative property of addition in 2 + 4n

8m + 14 - 12 + 4n = 8m + 4n + 2

Hence, the expression equivalent to 8m + 14 - 12 + 4n is** ****8m + 4n + 2**

**Problem 5 : **

Simplify the expression 6x² + 4(x² - 1)

**Solution :**

Use distributive property in 4(x² - 1)

6x² + 4(x² - 1) = 6x² + 4(x²) - 4(1)

6x² + 4(x² - 1) = 6x² + 4x² - 4

Use distributive property in 6x² + 4x²

6x² + 4(x² - 1) = (6 + 4)x² - 4

Add inside parenthesis

6x² + 4(x² - 1) = 10x² - 4

Hence, the expression equivalent to 6x² + 4(x² - 1) is** 10x² - 4 **

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