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 $large fn_cm 9x^2-10xy-5xy^2,3x^2+15xy-2xy^2,-2x^2+3xy^2-2xy$
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

Question : 2

Add $large fn_cm 41x^2-6xy+12y^2$ and $large 11x^2+2xy-7y^2$
A. $large 52x^2-4xy+5y^2$		B. $large 55^2+2x-6y$
C. $large 55^2+5yx-7y^2$		D. $large dpi{150} large 52x^2+4xy+5y^2$
Right Option : A
View Explanation

Question : 3

Add the given expressions: $6a^2+17b-5b^2 ;;; , -2a^2-20ab+2b^2 , ;;; 5a^2+2b-3b^2$
A. $large 9a^2-6b^2-ab$
B. $large 9a^2+6b^2-ab$
C. $large -9a^2-6b^2-ab$
D. $large 9a^2-6b^2+ab$
Right Option : A
View Explanation

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