**Generating equivalent algebraic expressions :**

An algebraic expression is a mathematical sentence involving constants (any real number), variables and the algebraic operations (addition, subtraction, multiplication, division and exponentiation by an exponent that is a rational number).

Let us consider the algebraic expression which is given below.

7(x - 3) + 2(2x - 5) - 3(x - 5) --------- (1)

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 to (1) is (8x - 16)

**Example 1 :**

Write the equivalent algebraic expression for the function defined by

f(x) = (x² - 5x + 6) / (x - 3)

**Solution :**

**Example 2 : **

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

**Example 3 : **

Write the equivalent algebraic expression for the function defined by

f(x) = (5x + 20) / (7x + 28)

**Solution: **

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

f(x) = 5(x + 4) / 7(x + 4)

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

f(x) = 5 / 7

**Example 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

**Example 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

**Example 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)

**Example 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

**Example 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 "Generating equivalent algebraic expressions".

Apart from the stuff given above, if you want to know more about "Generating equivalent algebraic expressions", please click here

Apart from stuff "Generating equivalent algebraic expressions", if you need any other stuff in math, please use our google custom search here.

HTML Comment Box is loading comments...

**WORD PROBLEMS**

**HCF and LCM word problems**

**Word problems on simple equations **

**Word problems on linear equations **

**Word problems on quadratic equations**

**Area and perimeter word problems**

**Word problems on direct variation and inverse variation **

**Word problems on comparing rates**

**Converting customary units word problems **

**Converting metric units word problems**

**Word problems on simple interest**

**Word problems on compound interest**

**Word problems on types of angles **

**Complementary and supplementary angles word problems**

**Markup and markdown word problems **

**Word problems on mixed fractrions**

**One step equation word problems**

**Linear inequalities word problems**

**Ratio and proportion word problems**

**Word problems on sets and venn diagrams**

**Pythagorean theorem word problems**

**Percent of a number word problems**

**Word problems on constant speed**

**Word problems on average speed **

**Word problems on sum of the angles of a triangle is 180 degree**

**OTHER TOPICS **

**Time, speed and distance shortcuts**

**Ratio and proportion shortcuts**

**Domain and range of rational functions**

**Domain and range of rational functions with holes**

**Graphing rational functions with holes**

**Converting repeating decimals in to fractions**

**Decimal representation of rational numbers**

**Finding square root using long division**

**L.C.M method to solve time and work problems**

**Translating the word problems in to algebraic expressions**

**Remainder when 2 power 256 is divided by 17**

**Remainder when 17 power 23 is divided by 16**

**Sum of all three digit numbers divisible by 6**

**Sum of all three digit numbers divisible by 7**

**Sum of all three digit numbers divisible by 8**

**Sum of all three digit numbers formed using 1, 3, 4**

**Sum of all three four digit numbers formed with non zero digits**