Addition of Algebraic Expression

Concept Explanation

Addition of Algebraic Expression

While adding algebraic expressions, we collect different groups of like terms and then simplify the coefficients of like terms in each group.

Illustration: Add: $7x^2- 4x+ 5, -3x^{2} + 2x - 1 ;;and ;;5x^{2}-x +9$

Solution : We are required to find the sum

= $(7x^{2}- 4x+ 5) + ( -3x^{2} + 2x - 1 ) + ( 5x^{2}-x +9 )$

= $7x^{2}- 3x^{2}+ 5x^{2}- 4x + 2x -x + 5 - 1 + 9$

= $left ( 7 - 3 + 5 right )x^{2} + left (- 4 + 2 - 1 right )x + left (5 - 1 + 9 right )$

= $9x^{2} - 3x + 13$

Illustration: Add: $5x^{2} - frac{1}{3} x +frac{5}{2},;; - frac{1}{2}x^{2} + frac{1}{2} x -frac{1}{3} ;;and; -2x^{2} + frac{1}{5} x -frac{1}{6}$

Solution: We are required to find the sum

$=(5x^{2}-frac{1}{3}x + frac{5}{2}) + (-frac{1}{2}x^{2}+ frac{1}{2}x -frac{1}{3}) + (-2x^{2}+ frac{1}{5}x - frac{1}{6})$

$=5x^{2} - frac{1}{2}x^{2} - 2x^{2} -frac{1}{3}x + frac{1}{2}x + frac{1}{5}x + frac{5}{2}- frac{1}{3} - frac{1}{6}$

$=left (5-frac{1}{2}-2 right ) x^{2} +left (-frac{1}{3} + frac{1}{2}+frac{1}{5}right ) x + left (frac{5}{2}- frac{1}{3} - frac{1}{6}right )$

$=left(frac{10-1-4}{2}right ) x^{2} + left (frac{-10+15+6}{30}right ) x + left(frac{15-2-1}{6}right )$

$=frac{5}{2} x^{2} + frac{11}{30} x + 2$

Sample Questions

(More Questions for each concept available in Login)

Question : 1

Add the given terms: $5x^2-2x-3 ;; , 10x^2-5 , ;; -7x^2+6x+9$
A. $8x^2-4x+1$	B. $8x^2+4x+1$	C. $-8x^2+4x+1$	D. $x^2+4x+1$
Right Option : B
View Explanation

Question : 2

Add: $4x^{2}y, -3xy^{2}, -5xy^{2}, 5x^{2}y$
A. $9x^{2}y - 10xy$	B. $8xy^{2} -9x^{2}y$	C. $9x^{2}y - 8xy^{2}$	D. $9xy^{2} - 8x^{2}y$
Right Option : C
View Explanation

Question : 3

Add: a + b - 3, b - a + 3, a - b + 3
A. a+b+c	B. a-b-3	C. a-b-c	D. a+b+3
Right Option : D
View Explanation

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Language - English

Chapters

Exponents and Power II

Prerequiste

Visualising Soild Shapes

Ratio and Proportion

Introduction to Trigonometry

Constructions

Quadrilaterals II

Quadrilaterals I

Linear Equations in One Variable II

Linear Equations in One Variable I

Cube and Cube Roots

Square and Square Root II

Square and Square Root I

Rational Numbers II

Rational Numbers I

Mensuration I

Exponents and Power I

Direct and Inverse Variation II

Direct and Inverse Variation I

Algebraic Expressions

Comparing Quantities III

Comparing Quantities II

Comparing Quantities I

Playing With Numbers

Introduction to Graphs

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