Question

Factorize each of the following expressions:
3√3a³ -b³ -5√5c³ -3√15abc

Answer 1

The algebraic expression is given as : 3√3a³ - b³ - 5√5c³ - 3√15abc

 

We can rewrite the  given expression as :  

(√3a)³ + (- b)³ + (-√5c)³ − 3(√3a)(b)(-√5c)

We know, a³ + b³ + c³ − 3abc = (a + b + c)(a² + b² + c²− ab − bc − ca)

=(√3a - b -√5c) { (√3a)² + (-b)² + (-√5c)²  −√3a × b − (b) ×  (-√5c)  −(- c) ×√3a}

= (√3a - b -√5c)  {3a² + b² + 5c² -√3ab -  √5bc  + √15ca}

Hence  the factors of 3√3a³ - b³ - 5√5c³ - 3√15abc is  (√3a - b -√5c)  {3a² + b² + 5c² -√3ab -  √5bc  + √15ca}.

HOPE THIS ANSWER WILL HELP YOU…..

 

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Answer 2

Answer:

Step-by-step explanation:

We can rewrite the  given expression as :  

(√3a)³ + (- b)³ + (-√5c)³ − 3(√3a)(b)(-√5c)

We know, a³ + b³ + c³ − 3abc = (a + b + c)(a² + b² + c²− ab − bc − ca)

=(√3a - b -√5c) { (√3a)² + (-b)² + (-√5c)²  −√3a × b − (b) ×  (-√5c)  −(- c) ×√3a}

= (√3a - b -√5c)  {3a² + b² + 5c² -√3ab -  √5bc  + √15ca}