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: 3mn , - 5mn , 8mn , - 4mn
A. 2mn	B. 4mn	C. 5mn	D. 8mn
Right Option : A
View Explanation

Question : 2

Add: $3a^2b - 4a^2b + 9a^2b$
A. $12a^2b$	B. $3a^2b$	C. $8a^2b$	D. 0
Right Option : C
View Explanation

Question : 3

Add $large fn_cm 9x^2-10xy-5xy^2,3x^2+15xy-2xy^2,-2x^2+3xy^2-2xy$
A. $large 11x^2+2xy-3x^2$	B. $large 10x^2+3xy-4xy^2$	C. $large 12x^2-3yx-5y^2$	D. None of these
Right Option : B
View Explanation

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