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

Jun 05, 2023

May 21, 2023

May 16, 2023

May 10, 2023

May 03, 2023

Latest Math Problems

May 09, 2023

A best free mathematics education website that helps students, teachers and researchers.

Learn each topic of the mathematics easily with understandable proofs and visual animation graphics.

A math help place with list of solved problems with answers and worksheets on every concept for your practice.

Copyright © 2012 - 2022 Math Doubts, All Rights Reserved