The value of $$2{a^3} - \left[ {3{a^3} + 4{b^3} - \left\{ {2{a^3} + \left( { - 7{a^3}} \right)} \right\}{\text{ + 5}}{a^3} - {\text{7}}{{\text{b}}^3}{\text{ }}} \right]{\text{ is - }}$$
A. $$ - 11{a^3}{\text{ + 3}}{{\text{b}}^3}$$
B. $${\text{7}}{{\text{b}}^3}{\text{ + 3}}{a^3}$$
C. $${\text{11}}{a^3} - 3{{\text{b}}^3}$$
D. $$ - \left( {11{a^3}{\text{ + 3}}{{\text{b}}^3}} \right)$$
Answer: Option A
Solution (By Examveda Team)
Given expression,$$ = 2{a^3} - \left[ {3{a^3} + 4{b^3} - \left\{ {2{a^3} + \left( { - 7{a^3}} \right)} \right\}{\text{ + 5}}{a^3} - {\text{7}}{{\text{b}}^3}{\text{ }}} \right]$$
$$\eqalign{ & = 2{a^3} - \left[ {3{a^3} + 4{b^3} - \left\{ { - 5{a^3}} \right\}{\text{ + 5}}{a^3} - {\text{7}}{{\text{b}}^3}{\text{ }}} \right] \cr & = 2{a^3} - \left[ {3{a^3} + 4{b^3}{\text{ + 5}}{a^3}{\text{ + 5}}{a^3} - {\text{7}}{{\text{b}}^3}{\text{ }}} \right] \cr & = 2{a^3} - \left[ {13{a^3} - 3{b^3}} \right] \cr & = 2{a^3} - 13{a^3} + 3{b^3} \cr & = - 11{a^3} + 3{b^3} \cr} $$
This Question Belongs to Arithmetic Ability >> Simplification
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