**Generating equivalent 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).

To generate equivalent expression to another expression, we have to be aware of the parts of an algebraic expression.

We can use properties to combine like terms in an expression.

For example, let us consider the algebraic expression

3x + 2x + 4

Use the Distributive Property to add the coefficients of the like terms (3x and 2x).

3x + 2x + 4 = (3 + 2)x + 4 = 5x + 4

When we rewrite an expression so that it has no parentheses and so that all like terms are combined, we are simplifying the expression.

**Example 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**

**Example 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**

**Example 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**

After having gone through the stuff given above, we hope that the students would have understood "How to generate equivalent expressions".

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

Apart from the stuff given in this section, 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**