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Like algebraic terms

The algebraic terms whose literal coefficients are the same, are called the like algebraic terms.

Introduction

The likeness of two or more algebraic terms are determined by their literal coefficients. If the literal coefficients of two or more algebraic terms are the same, then the algebraic terms are looked similar, and they are called as like algebraic terms. Therefore, the property of the likeness is a key point for determining the like algebraic terms in algebra.

Example

$-3xy$ and $6xy$ are two algebraic terms.

Observe the two algebraic terms closely and it seems they are similar. Let’s find the literal coefficients of them to confirm the property of likeness of them mathematically.

$-3xy = -3 \times xy$ and $6xy = 6 \times xy$

$xy$ is the literal coefficient of $-3$ for the first algebraic term and $xy$ is the literal coefficient of $6$ for the second algebraic term. The literal coefficients of them are the same. Hence, the two algebraic terms are looked similar and they are called as like algebraic terms.

Examples

Observe the following examples to understand like algebraic terms much better.

$(1) \,\,\,$ $a$, $-6a$

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

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

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

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