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:   5m -7n, 3n -4m +2, 2m - 3mn  -5

Right Option : A
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Explanation
Question : 2

Add:    7x^2+3x ;;; and ;;; 9x-5x^2

Right Option : C
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Explanation
Question : 3

Add:  14x + 10y - 12xy -13, 18 -7x -10y + 8xy, 4xy

Right Option : B
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Explanation
 
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