Subtraction of Unlike Algebraic terms

subtracting unlike terms

Definition

A mathematical operation of subtracting an algebraic term from another different algebraic term is called subtraction of unlike algebraic terms.

Unlike algebraic terms do not consist of a common literal coefficient and the property makes subtraction of an algebraic term of another impossible. However, the subtraction of two unlike terms form an algebraic expression.

Procedure

$2a^{\displaystyle 2}b^{\displaystyle 2}$ and $6ab$ are two algebraic terms. The literal coefficients of $2a^{\displaystyle 2}b^{\displaystyle 2}$ and $6ab$ are $a^{\displaystyle 2}b^{\displaystyle 2}$ and $ab$ respectively. Due to having different literal coefficients, it is not possible to subtract an algebraic term from another algebraic term. However, they can be subtracted to form an algebraic expression.

Assume, $2a^{\displaystyle 2}b^{\displaystyle 2}$ is subtracted from $6ab$. Therefore, write $6ab$ first and then $2a^{\displaystyle 2}b^{\displaystyle 2}$ but place a minus sign between them to represent the subtraction of them.

$6ab \,- 2a^{\displaystyle 2}b^{\displaystyle 2}$

This algebraic expression represents the subtraction of $2a^{\displaystyle 2}b^{\displaystyle 2}$ from $6ab$.

Similarly, subtract $6ab$ from $2a^{\displaystyle 2}b^{\displaystyle 2}$.

$2a^{\displaystyle 2}b^{\displaystyle 2} \,- 6ab$

It represents the subtraction of $6ab$ from $2a^{\displaystyle 2}b^{\displaystyle 2}$.

Examples

Look at the below examples to know how to subtract two unlike terms algebraically.

$(1) \,\,\,$ $a \,-\, b$

$(2) \,\,\,$ $7m^{\displaystyle 2} \,- 2n^{\displaystyle 2}$

$(3) \,\,\,$ $5xy \,\,–\, 5x^{\displaystyle 2}y$

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