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**Simplify Algebraic Expressions**

**Simplify of algebraic expressions**is the addition and subtraction of the terms of expressions. To

**simplify the algebraic expressions**we need first to understand about the addition and subtraction of algebraic expressions.

###
**Addition**

In the addition of algebraic expression,
we should add the coefficients of the like terms of the expression only. We can
not add the coefficients of unlike terms.

__For example__**:**

- x + x + 2x = 4x

- 3y + 7y + 2z = 10y + 2z

- 3a2 + 5a2 + 2a = 8a2 + 2a

###
**Subtraction**

In the subtraction of algebraic
expression, we should subtract the coefficients of the like terms of the
expression only. We can not subtract the coefficient of unlike terms.

__For example__**:**

- 7a – 3a = 4a

- 5x

^{2}– 3x^{2}= 2x^{2}
- 4y

^{2}– 2y – 3y^{2}= y^{2}– 2y###
**Addition and subtraction of two or more algebraic expressions**

For the addition or subtraction of two or
more than two algebraic expressions having two or more than two terms, we can
add or subtract the terms of the algebraic expressions in vertical or horizontal
arrangement. We should use the following steps:

*- Arrange the like terms in the same column at first.*

*-*

*After that we add or subtract their coefficients.*

Study the following worked out examples:

###
*Workout
Examples*

*Workout Examples*

*Example 1: Add: 3x*^{2}+ 5xy – 2y^{2}and 7x^{2}+ 5y^{2}+ 3xy

*Solution:*

*Addition by vertical arrangement:*

*Addition by horizontal arrangement:*

*3x*^{2}+ 5xy – 2y^{2}+ 7x^{2}+ 5y^{2}+ 3xy

*= 3x*^{2}+ 7x^{2}+ 5xy + 3xy – 2y^{2}+ 5y^{2}

*= 10x*^{2}+ 8xy + 3y^{2}

*Example 2: Add: 4b*^{2}+ 3ab, 5a^{2}+ 5ab and 3a^{2}+ 6ab + 7b^{2}

*Solution:*

*Addition by vertical arrangement:*

*Addition by horizontal arrangement:*

*4b*^{2}+ 3ab + 5a^{2}+ 5ab + 3a^{2}+ 6ab + 7b^{2}

*= 4b*^{2}+ 7b^{2}+ 3ab + 5ab + 6ab + 5a^{2}+ 3a^{2}

*= 11b*^{2}+ 14ab + 8a^{2}

*Example 3: Subtract 3ab – 4bc + 8 from 7ab + 3bc - 4*

*Solution:*

*Subtraction by vertical arrangement:*

*Subtraction by horizontal arrangement:*

*7ab + 3bc – 4 – (3ab – 4bc + 8)*

*= 7ab + 3bc – 4 – 3ab + 4bc – 8*

*= 7ab – 3ab + 3bc + 4bc – 4 – 8*

*= 4ab + 7bc – 12*

*Example 4: What should be added to 3x + 4y + 5z to get 8x + y – 4z?*

*Solution:*

*[ To solve this problem, let’s think first, what should be added to 6 to get 14? In 6, we should add 8 to get 14. And 8 is the difference of 14 and 6, i.e. 14 – 6 = 8. It is very good idea, and we use this idea in algebra also. So we should subtract 3x + 4y + 5z from 8x + y – 4z.]*

*Now,*

*∴*

*The required expression to be added is 5x – 3y – 9z.*

*Example 5: What should be subtracted from 4x – 7y + 4z to get 2x + 5y + 5z?*

*Solution:*

*[ To solve this problem, let’s think first, what should be subtracted from 9 to get 5? Obviously 4 should be subtracted. And 4 is the difference of 9 and 5, i.e. 9 – 5 = 4. It is very good idea, and we use this idea in algebra also. So we should subtract 2x + 5y + 5z from 4x – 7y + 4z.]*

*Now,*

*∴*

*The required expression to be subtracted is 2x – 12y –z.*

*Example 6: Simplify: 10x*^{2}– 2(x^{2}+ 3x – 6) – x(x + 2)

*Solution:*

*Here,*

*10x*^{2}– 2(x^{2}+ 3x – 6) – x(x + 2)

*= 10x*^{2}– 2x^{2}– 6x + 12 – x^{2}– 2x

*= 10x*^{2}– 2x^{2}– x^{2}– 6x – 2x + 12

*= 7x*^{2}– 8x + 12

*Example 7: Simplify: 2x(x – 3y) – 3y(x + 2y) – 2(x*^{2}+ xy)

*Solution:*

*Here,*

*2x(x – 3y) – 3y(x + 2y) – 2(x*^{2}+ xy)

*= 2x*^{2}– 6xy – 3xy – 6y^{2}– 2x^{2}– 2xy

*= 2x*^{2}– 2x^{2}– 6xy – 3xy – 2xy – 6y^{2}

*= – 11xy – 6y*^{2}

*You can comment your questions or problems regarding the*

**algebraic simplification**here.
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