A mathematical operation of subtracting an algebraic term from its like algebraic term is called the subtraction of like algebraic terms.

The like algebraic terms often involve in subtraction to subtract an algebraic term from another. Actually, the like algebraic terms have the same literal factor commonly. Hence, it is possible to subtract an algebraic term from another easily but the subtraction of them is also an algebraic term and it is in the same form of the like algebraic terms.

$2x^2y$ and $5x^2y$ are two two like algebraic terms.

01

Take, the algebraic term $5x^2y$ is subtracted from its like term $2x^2y$. So, write $2x^2y$ first, then $5x^2y$ but display a negative sign $(-)$ between them to express subtraction mathematically.

$2x^2y-5x^2y$

02

The like algebraic terms have a common literal factor $x^2y$. So, it can be taken common from them.

$\implies 2x^2y-5x^2y = (2-5)x^2y$

Now, perform the subtraction of the numbers and multiply it by the literal factor of them.

$\implies 2x^2y-5x^2y = -3x^2y$

The subtraction of them is an algebraic term and it is also in the same of the like algebraic terms. The example has proved that the subtraction of like algebraic terms is also a like algebraic term.

Observe the following examples to know how to subtract an algebraic term from its like algebraic term mathematically.

$(1)\,\,\,\,\,\,$ $7a-5a$ $\,=\,$ $(7-5)a$ $\,=\,$ $2a$

$(2)\,\,\,\,\,\,$ $2bc-10bc$ $\,=\,$ $(2-10)bc$ $\,=\,$ $-8bc$

$(3)\,\,\,\,\,\,$ $3c^2-2c^2$ $\,=\,$ $(3-2)c^2$ $\,=\,$ $c^2$

$(4)\,\,\,\,\,\,$ $17d^3e^2f-23d^3e^2f$ $\,=\,$ $(17-23)d^3e^2f$ $\,=\,$ $-6d^3e^2f$

$(5)\,\,\,\,\,\,$ $5ghi-ghi$ $\,=\,$ $(5-1)ghi$ $\,=\,$ $4ghi$

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