Question

a square minus b square ka whole cube plus b square minus C square whole cube + x square minus A square whole cube divided by minus b whole cube plus B minus C whole cube plus B minus C whole cube is equal to a + b + c c plus a proof​

Answer 1

Answer:

(a + b)(b + c)(c + a)

Step-by-step explanation:

((a² - b²)³  + (b² - c²)³ + (c² - a²)³ ) / ((a - b)³ + (b-c)³ + (c - a)³)

Numerator

= (a² - b²)³  + (b² - c²)³ + (c² - a²)³

using the fact

if x+y+z = 0, then x³+y³+ z³ = 3 x y z

x = a² - b²

y = b² - c²

z = c² - a²

x + y + z = 0  ( as a² - b² +b² - c² + c² - a²) = 0

= 3 (a² - b²) (b² - c²) (c² - a²)

= 3 (a + b)(a - b)(b + c)(b-c)(c + a)(c-a)

similarly denominator =

((a - b)³ + (b-c)³ + (c - a)³) = 3(a-b)(b-c)(c-a)

as here x = a-b  , y = b-c , z = c-a    & x + y + z = 0

numerator/Denominator

= 3 (a + b)(a - b)(b + c)(b-c)(c + a)(c-a)/ 3(a-b)(b-c)(c-a)

= (a + b)(b + c)(c + a)

((a² - b²)³  + (b² - c²)³ + (c² - a²)³ ) / ((a - b)³ + (b-c)³ + (c - a)³) = (a + b)(b + c)(c + a)