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.

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

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

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

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

Write the like algebraic terms of all expressions closer.

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

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.

Latest Math Topics

Latest Math Problems

Email subscription

Math Doubts is a best place to learn mathematics and from basics to advanced scientific level for students, teachers and researchers.
Know more

Learn how to solve easy to difficult mathematics problems of all topics in various methods with step by step process and also maths questions for practising.