**Equivalent algebraic expressions worksheet :**

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

1. Write the equivalent algebraic expression for

7(x - 3) + 2(2x - 5) - 3(x - 5)

2. Write the equivalent algebraic expression for the function defined by

f(x) = (x² - 5x + 6) / (x - 3)

3. Write the equivalent algebraic expression for the expression given below.

4x - (2 + 4x) - 2 (x - 1) - 8 (x -3)

4. Write the equivalent algebraic expression for the expression given below.

(2x - 7)/5 + (x + 9)/15 - (2x -2)/5

5. Write the equivalent algebraic expression for the expression given below.

(3x+41)/2 + (x-3 )/5 -(9-2x)/6

6. Write the equivalent algebraic expression for the function defined by

f(x) = (6x² - 54) / (x² + 7x + 12)

7. Write the equivalent algebraic expression for the function defined by

f(x) = (64a³ + 125b³) / (4a²b + 5ab²)

8. Write the equivalent algebraic expression for the function defined by

f(x) = (x² + 7x + 10) / (x² - 4)

**Problem 1 :**

Write the equivalent algebraic expression for

7(x - 3) + 2(2x - 5) - 3(x - 5)

**Solution :**

To generate equivalent algebraic expression, we have to simplify.

Let us simplify the expression as given below.

**Step 1 :**

Distributing the number which is outside the parenthesis with inner terms.

= 7x - 21 + 4x - 10 - 3x + 15

**Step 2 :**

Combine the like terms

= 7x + 4x - 3x - 21 - 10 + 15

= 11x - 3x - 31 + 15

= 8x - 16

Hence, equivalent algebraic expression is (8x - 16)

**Problem 2 :**

Write the equivalent algebraic expression for the function defined by

f(x) = (x² - 5x + 6) / (x - 3)

**Solution :**

**Problem 3: **

Write the equivalent algebraic expression for the expression given below.

4x - (2 + 4x) - 2 (x - 1) - 8 (x -3)

**Solution:**

= 4x - (2 + 4x) - 2 (x - 1) - 8 (x -3)

= 4x - 2 - 4x - 2x + 2 - 8x + 24

= 4x - 4x - 2x - 8x - 2 + 2 + 24

= -10x + 24

**Problem 4 : **

Write the equivalent algebraic expression for the expression given below.

(2x - 7)/5 + (x + 9)/15 - (2x -2)/5

**Solution :**

= (2 x - 7)/5 + (x + 9 )/15 - (2 x - 2 )/5

Now we are going to combine the like terms

**Problem 5 : **

Write the equivalent algebraic expression for the expression given below.

(3x+41)/2 + (x-3 )/5 -(9-2x)/6

**Solution :**

Now we are going to distribute the numbers which is out side the parenthesis to the inner terms.Then combine the like terms

**Problem 6 : **

Write the equivalent algebraic expression for the function defined by

f(x) = (6x² - 54) / (x² + 7x + 12)

**Solution: **

Factoring the numerator and denominator of the given rational function, we get

f(x) = 6(x² - 9) / (x + 3)(x + 4)

f(x) = 6(x² - 3²) / (x + 3)(x + 4)

f(x) = 6(x + 3)(x - 3) / (x + 3)(x + 4)

Getting rid of the common factor (x + 3) at both numerator and denominator, we get

f(x) = 6(x-3) / (x + 4)

**Problem 7 : **

Write the equivalent algebraic expression for the function defined by

f(x) = (64a³ + 125b³) / (4a²b + 5ab²)

**Solution: **

**f(x) = (64a³ + 125b³) / (4a²b + 5ab²) **

**f(x) = (4****³****a³ + 5****³b****³) / (4a²b + 5ab²) **

**f(x) = [(4****a)³ + (5****b)****³] / (4a²b + 5ab²) **

Factoring the numerator and denominator of the given rational function, we get

f(x) = [4a + 5b][(4a)² - 4a.5b + (5b)²] / ab(4a + 5b)

f(x) = [(4a)² - 4a.5b + (5b)²] / ab

f(x) = [16a² - 20ab + 25b²] / ab

Getting rid of the common factor (4a + 5b) at both numerator and denominator, we get

f(x) = [(4a)² - 4a.5b + (5b)²] / ab

f(x) = [16a² - 20ab + 25b²] / ab

**Problem 8 : **

Write the equivalent algebraic expression for the function defined by

f(x) = (x² + 7x + 10) / (x² - 4)

**Solution: **

f(x) = (x² + 7x + 10) / (x² - 4)

f(x) = (x² + 7x + 10) / (x² - 2²)** **

Factoring the numerator and denominator of the given rational function, we get

f(x) = (x + 2)(x + 5) / (x + 2)(x - 2)

Getting rid of the common factor (x + 5) at both numerator and denominator, we get

f(x) = (x + 5) / (x - 2)

After having gone through the stuff given above, we hope that the students would have understood "Equivalent algebraic expressions worksheet".

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