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Addition of Algebraic expressions

A mathematical operation of adding two or more algebraic expressions is called the addition of algebraic expressions. It is also called as the summation of the algebraic expressions.


Two or more algebraic expressions are often involved in addition to find the sum of them. In algebra, the addition of algebraic expressions is performed by displaying a plus sign between every two algebraic expressions. Then, the like algebraic terms of them are added to get the summation of the algebraic expressions.

  1. $-17x^2-2xy+23y^2$
  2. $-9y^2+15x^2+7xy$
  3. $13x^2+3y^2-4xy$

First step

Write all algebraic expressions in a row by displaying a plus sign between every two expressions.

$(-17x^2-2xy+23y^2)$ $+$ $(-9y^2+15x^2+7xy)$ $+$ $(13x^2+3y^2-4xy)$

$= \,\,\,$ $-17x^2-2xy+23y^2$ $-9y^2+15x^2+7xy$ $+$ $13x^2+3y^2-4xy$

Second step

Write the like algebraic terms of all expressions closer.

$= \,\,\,$ $-17x^2$ $+$ $15x^2$ $+$ $13x^2$ $+$ $23y^2$ $-$ $9y^2$ $+$ $3y^2$ $-$ $2xy$ $+$ $7xy$ $-$ $4xy$

Third step

Now, combine the like algebraic terms by adding or subtracting the like terms.

$= \,\,\,$ $(-17x^2+15x^2+13x^2)$ $+$ $(23y^2-9y^2+3y^2)$ $+$ $(-2xy+7xy-4xy)$

$= \,\,\,$ $(-2x^2+13x^2)$ $+$ $(14y^2+3y^2)$ $+$ $(5xy-4xy)$

$= \,\,\,$ $11x^2+17y^2+xy$

The summation is a trinomial and its unlike algebraic terms cannot be added. Therefore, the sum of the algebraic expressions is simply represented by their simplified algebraic expression. Thus, the algebraic expressions are added in algebra.

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