Addition And Subtraction Of Algebraic Expression

Algebraic expression addition and subtraction are slightly more complicated than natural number operations. In order to learn the addition and subtraction of algebraic expressions, first we have to understand the algebraic expression. An algebraic expression is just an equation containing a combination of constants and variables.

Let us take an example of algebraic expression: suppose your teacher asked you to convert the statement “Marks obtained by student A of class 10th is 10 marks more than the marks obtained by student B of 10th “ into mathematical form.

Now to express it in mathematical form suppose marks obtained by A are x and marks obtained by B are y now according to the statement x is 10 more than y.

In mathematical form, we write the above statement as

x=y+10

This expression is known as an Algebraic expression.

Algebraic Expressions Addition And Subtraction

In mathematics addition, subtraction and other mathematical operations are easily applicable to natural numbers. If we talk about mathematical operations on algebraic expressions it is not the same as in natural numbers. While applying addition and subtraction to algebraic expressions we must keep in mind that only terms which are having the same variable and exponent will be added or subtracted. We have to follow some steps for applying mathematical operations to an algebraic expression.

Methods of addition and subtraction are:

1. Horizontal

2. Vertical

Horizontal Addition

Steps in addition

1. Write each algebraic expression within a bracket in a single row with a plus sign in between them.

2. Now open all the brackets.

3. Write terms having the same variable and exponent with the appropriate sign in a bracket.

4. Add the coefficient of all the terms having the same variable and exponent.

To understand the above steps let us take an example of algebraic addition

First expression- \[2x + 3y + 1\]

Second expression- \[10x + 13y + 5\]

Follow above steps

1. \[(2x + 3y + 1) + (10x + 13y + 5)\]

2. \[2x + 3y + 1 + 10x + 13y + 5\]

3. \[(2x + 10x) + (3y + 13y) + (1 + 6)\]

4. \[12x + 16y + 6\]

Vertical Addition

In this method, we have to write each expression in a different row. While writing expressions in different rows keep in mind that the terms having the same variables and exponent must be written one below the others along with their sign. Now we have to add all coefficients present in a particular column to get the value of the addition.

To understand the above steps let us take an example of algebraic addition

First expression- \[2x + 3y + 1\]

Second expression-\[10x + 13y + 5\]

Now add these two by using the vertical method

\begin{array}{ccc}

+2 x & +3 y & +1 \\

+10 x & +13 y & +5 \\

12 x & +16 y & +6

\end{array}

Horizontal Subtraction

Steps in subtraction

1. Write each algebraic expression within a bracket in a single row with a minus sign in between them.

2. Now open all brackets and apply the algebra of the sign of a term.

3. Write terms having the same variable and exponent with the appropriate sign in a bracket.

4. Subtract the coefficient of all the terms having the same variable and exponent.

To understand the above steps let us take an example of algebraic addition

First expression-

Second expression-

Now subtract first from second by using the horizontal method

Follow above steps

First expression- \[2x + 3y + 1\]

Second expression- \[10x + 13y + 5\]

Follow above steps

5. \[(2x + 3y + 1) - (10x + 13y + 5)\]

6. \[2x + 3y + 1 - 10x - 13y - 5\]

7. \[(2x - 10x) + (3y - 13y) + (1 - 5)\]

8. \[ - 8x - 10y - 4\]

Vertical Subtraction

In this method, we have to write each expression in a different row. While writing expressions in different rows keep in mind that the terms having the same variables and exponent must be written one below the others along with their sign. Now we have to subtract all coefficients present in a particular column to get the value of the addition.

Let us take an example to understand it

First expression-

Second expression-

Now subtract first from second by using the vertical method

First expression- \[2x + 3y + 1\]

Second expression- \[10x + 13y + 5\]

Now subtract first from second by using vertical method

\begin{array}{ccc}

+2 x & +3 y & +1 \\

-(10 x & +13 y & +5) \\

-8 x & -10 y & -4

\end{array}