Like Algebraic Terms

like terms

Definition

The algebraic terms having same literal coefficient are called like algebraic terms or simply like terms.

Algebraic terms are mainly formed by the product of combination of numbers and symbols. In some cases, two or more algebraic terms are having same literal coefficient. This property makes all the algebraic terms look similar. Hence, the algebraic terms which have common literal coefficient are known as like algebraic terms. They are simply called as like terms.

Example

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

  1. The first algebraic term is $3x{y}^{\displaystyle 2}$ and the literal coefficient in this term is $x{y}^{\displaystyle 2}$.
  2. The second algebraic term is $-8x{y}^{\displaystyle 2}$ and the literal coefficient in this term is $x{y}^{\displaystyle 2}$.
  3. The third algebraic term is $\Bigg(\dfrac{2}{7}\Bigg) x{y}^{\displaystyle 2}$ and the literal coefficient is $x{y}^{\displaystyle 2}$ in this term.
  4. The fourth algebraic term is $0.8x{y}^{\displaystyle 2}$ and the literal coefficient is $x{y}^{\displaystyle 2}$ in this term.

In all the algebraic terms, the literal coefficient is same but numeral coefficients are different. However, they appear as similar terms due to the common literal coefficient $x{y}^{\displaystyle 2}$. Therefore, the four algebraic terms are like terms.

Examples

Observe the following more examples to understand like terms much better in algebra.

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

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

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

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

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

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