Find the sum ( 5 8 x 3 + 2 ) + ( 5 16 x 3 − 5 ) \left( \frac { 5 } { 8 } x ^ { 3 } + 2 \right) + \left( \frac { 5 } { 16 } x ^ { 3 } - 5 \right) ( 8 5 x 3 + 2 ) + ( 16 5 x 3 − 5 ) .A) 15 16 x 3 − 3 \frac { 15 } { 16 } x ^ { 3 } - 3 16 15 x 3 − 3 B) 15 16 x 6 − 3 \frac { 15 } { 16 } x ^ { 6 } - 3 16 15 x 6 − 3 C) 15 x 3 − 48 15 x ^ { 3 } - 48 15 x 3 − 48 D) 15 x 6 − 48 15 x ^ { 6 } - 48 15 x 6 − 48 E) 15 16 x 9 − 3 \frac { 15 } { 16 } x ^ { 9 } - 3 16 15 x 9 − 3

Question

Find the sum   ( 5 8 x 3 + 2 )  + ( 5 16 x 3 − 5 )  \left( \frac { 5 } { 8 } x ^ { 3 } + 2 \right)  + \left( \frac { 5 } { 16 } x ^ { 3 } - 5 \right)  ( 8 5 ​ x 3 + 2 )  + ( 16 5 ​ x 3 − 5 )    .A)    15 16 x 3 − 3 \frac { 15 } { 16 } x ^ { 3 } - 3 16 15 ​ x 3 − 3 B)    15 16 x 6 − 3 \frac { 15 } { 16 } x ^ { 6 } - 3 16 15 ​ x 6 − 3 C)    15 x 3 − 48 15 x ^ { 3 } - 48 15 x 3 − 48 D)    15 x 6 − 48 15 x ^ { 6 } - 48 15 x 6 − 48 E)    15 16 x 9 − 3 \frac { 15 } { 16 } x ^ { 9 } - 3 16 15 ​ x 9 − 3

Caroline Ayman · Accepted Answer

Final Answer : A, Explanation :   To find the sum, add the like terms:   5 8 x 3 + 5 16 x 3 = 10 16 x 3 + 5 16 x 3 = 15 16 x 3 \frac{5}{8}x^3 + \frac{5}{16}x^3 = \frac{10}{16}x^3 + \frac{5}{16}x^3 = \frac{15}{16}x^3 8 5 ​ x 3 + 16 5 ​ x 3 = 16 10 ​ x 3 + 16 5 ​ x 3 = 16 15 ​ x 3   and   2 − 5 = − 3 2 - 5 = -3 2 − 5 = − 3  , resulting in   15 16 x 3 − 3 \frac{15}{16}x^3 - 3 16 15 ​ x 3 − 3  .

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