GENERATING EQUIVALENT EXPRESSIONS WORKSHEET

About "Generating equivalent expressions worksheet"

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" 

Generating equivalent expressions worksheet

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)

Generating equivalent expressions - Examples

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  =  2

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

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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