Subtraction of Like Algebraic terms

subtracting like terms

Definition

A mathematical operation of subtracting an algebraic term from another similar algebraic term is called subtraction of like algebraic terms.

Like algebraic terms contain a common literal coefficient and it is possible to subtract an algebraic term from another like term by this property. Two like algebraic terms are subtracted and form another like term due to having same literal coefficient.

Procedure

$6x^{\displaystyle 2}yz$ and $8x^{\displaystyle 2}yz$ are two algebraic terms. The literal coefficient of both algebraic terms is same and it is $x^{\displaystyle 2}yz$. So, the two algebraic terms are like algebraic terms and subtraction between them is called the subtraction of like algebraic terms.

Assume, the term $6x^{\displaystyle 2}yz$ is subtracted from $8x^{\displaystyle 2}yz$. So, write $8x^{\displaystyle 2}yz$ first and then $6x^{\displaystyle 2}yz$ but place a minus sign ($-$) between them to represent subtraction between them.

$8x^{\displaystyle 2}yz \,- 6x^{\displaystyle 2}yz$

Take literal coefficient $x^{\displaystyle 2}yz$ common from both terms.

$\implies 8x^{\displaystyle 2}yz \,- 6x^{\displaystyle 2}yz = (8 \,–\, 6)x^{\displaystyle 2}yz$

$\therefore \,\, 8x^{\displaystyle 2}yz \,- 6x^{\displaystyle 2}yz = 2x^{\displaystyle 2}yz$

Similarly, assume the term $8x^{\displaystyle 2}yz$ is subtracted from $6x^{\displaystyle 2}yz$. So, write $6x^{\displaystyle 2}yz$ first and then $8x^{\displaystyle 2}yz$ and place a minus sign ($-$) between them to denote the subtraction of them.

$6x^{\displaystyle 2}yz \,- 8x^{\displaystyle 2}yz$

$\implies 6x^{\displaystyle 2}yz \,- 8x^{\displaystyle 2}yz = (6 \,- 8)x^{\displaystyle 2}yz$

$\therefore \,\, 6x^{\displaystyle 2}yz \,- 8x^{\displaystyle 2}yz = \,- 2x^{\displaystyle 2}yz$

Examples

Observe the following examples to understand how to subtract two like terms algebraically.

$(1) \,\,\,$ $5m \,-\, 5m = 0$

$(2) \,\,\,$ $7p^{\displaystyle 2}q^{\displaystyle 4} \,- 6p^{\displaystyle 2}q^{\displaystyle 4} = p^{\displaystyle 2}q^{\displaystyle 4}$

$(3) \,\,\,$ $2ab \,- 10ab = -8ab$

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