Unlike algebraic terms

The algebraic terms which have different literal factors are called unlike algebraic terms.

unlike terms

Introduction

Every algebraic term is formed to represent a quantity in terms of one or more literals. There is no rule that two or more algebraic terms should be in same form. If two or more algebraic terms do not have any match, then they are called unlike algebraic terms.

The property of unlikeness of two or more algebraic terms is determined by comparing the literal factor of a term with the literal factor of another term.

Example

$2xy$, $-4x^2y$, $\Bigg(\dfrac{3}{8}\Bigg)xy^2$ and $0.125x^2y^2$ are four algebraic terms.

$xy$ is the literal factor of $2xy$, $x^2y$ is the literal factor of $-4x^2y$, $xy^2$ is the literal factor of $\Bigg(\dfrac{3}{8}\Bigg)xy^2$ and $x^2y^2$ is the literal factor of $0.125x^2y^2$. Compare all four literal factors and there is no matching between them. The unlikeness of literal factors of them is classified them as the unlike algebraic terms.

Remember, $2$, $-4$ and $\dfrac{3}{8}$ and $0.125$ are the numerical factors of the above algebraic terms respectively but they do not consider to determine the unlikeness of the terms because they do not belong to algebra and they are numbers.

Examples

Look at the following more examples to understand unlike terms much clearly in algebra.

$(1) \,\,\,$ $2a$, $2b$, $2c$

$2$ is the numerical coefficient of all terms commonly but it is not considered to determine the unlikeness of the terms. So, check the literal factors of them. $a$, $b$ and $c$ are literal factors of the three terms respectively and they are not same. Hence, the three algebraic terms are unlike terms.

$(2) \,\,\,$ $l^2$, $\dfrac{l}{7}$, $5.5l^3$

$l^2$ is the literal coefficient of the first term, $l$ is the literal coefficient of second term and $l^3$ is the literal coefficient of third term. All three factors are not same even though all three factors are formed by the same literal. Hence, they are unlike algebraic terms.

$(3) \,\,\,$ $-6m$, $4n$, $5mn$, $8m^2n$

The literal factors of the above four terms are $m$, $n$, $mn$ and $m^2n$ respectively. Therefore, they are known as unlike algebraic factors.

$(4) \,\,\,$ $5p^3q^2r$, $5p^3qr^2$, $5pq^3r^2$

The numerical factor is $5$ for all of them and it seems the literal factors are similar but not same exactly. $p^3q^2r$, $p^3qr^2$ and $pq^3r^2$ are factors and there is a lot of difference between them. Hence, they are unlike algebraic terms.

$(5) \,\,\,$ $xy$, $3yz$, $-3zx$, $5xyz$, $3z$

In this example, $xy$, $yz$, $zx$, $xyz$ and $z$ are literal factors of the five algebraic terms but they are unlike. Hence, the five algebraic terms are called unlike algebraic terms.



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