Question

39. Simplify/
(343 x 343 x 343 - 113 x 113 x 113)/
( 343 x 343 + 343 x 113 + 113 x 113)
a. 340
b. 300
c. 230
d. 200​

Answer 1

Answer:

We know

$a {}^{3} - b {}^{3} = (a - b)(a {}^{2} + ab + b {}^{2} )$

Here

a = 343 and b = 113

Putting the value

We get,

$\frac{(343 \times 343 \times 343 - 113 \times 113 \times 113)}{(343 \times 343 + 343 \times 113 + 113 \times 113)} \\ = \frac{(343 {}^{3} - 113 {}^{3} )}{(343 {}^{2} + 343 \times 113 + 113 {}^{2} ) } \\ = \frac{(343 - 113)(343 {}^{2} + 343 \times 113 + 113 {}^{2} ) }{(343 {}^{2} + 343 \times 113 + 113 {}^{2} ) } \\ = 343 - 113 \\ = 230$

So, option c) 230 is correct answer.