Like algebraic terms

The algebraic terms which have same literal factors are called like algebraic terms.

like terms

Introduction

An algebraic term is formed to represent a quantity in terms of one or more literals. In some cases, an algebraic term matches with another algebraic term or terms. It is possible in the case of two or more algebraic terms.

If an algebraic term matches with another algebraic term or terms, then they are called like algebraic terms. It is possible only if the literal factors of two or more algebraic terms are same.

Example

$3xy^2$, $-8xy^2$, $\Bigg(\dfrac{2}{7}\Bigg) xy^2$ and $0.8xy^2$ are four algebraic terms.

Compare each term with another and all four terms have the similarly but there is a slight change. In other words, $xy^2$ is a common literal factor in all four algebraic terms but they have different numerical factors.

Actually, there is no importance for the numerical factors of algebraic terms in the sense of algebra because it is algebra. Hence, the four algebraic terms are called like algebraic terms.

More Examples

Look at the following example to have perfect knowledge on identifying the like algebraic terms algebraically.

$(1) \,\,\,$ $a$, $-6a$
In this case, The numerical factors of both terms are $1$ and $-6$ respectively but $a$ is the common literal factor of them. Hence, they are like algebraic terms.

$(2) \,\,\,$ $l^2$, $\dfrac{l^2}{5}$, $-0.25l^2$

In this example, $1$, $\dfrac{1}{5}$ and $-0.25$ are numerical factors respectively but $l^2$ is the common literal factor. So, they are called like algebraic terms.

$(3) \,\,\,$ $4mn$, $-6mn$, $7mn$, $9mn$

$4$, $-6$, $7$ and $9$ are different numerical factors of the above four algebraic terms respectively but $mn$ is the common literal factor of them. Hence, they are known as like algebraic terms.

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

The two algebraic terms are like algebraic terms because they have $p^3q^2r$ as literal factor commonly and the numerical factors $1$ and $5$ are not considered.

$(5) \,\,\,$ $-xyz$, $6xyz$, $-10xyz$, $26xyz$, $-276xyz$

In this example, $-1$, $6$, $-10$, $26$ and $-276$ are numerical factors but xyz is the common literal factor. Hence, they are in same form and therefore they are called like algebraic terms.

Therefore, the literal factor is the only considerable factor to determine the property of likeness of algebraic terms.



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