Question

Give answer of question number 25

Answer 1

Given expression is

3√3a^3 - b^3 -5√5c^3 - 3 √15abc

now
3 can be written as √3 ×√3 and 5 as √5 ×√5
also √15 can be written as , √3 × √5

therefore equation becomes ,
√3 ×√3 × √3 ×a^3 - b^3 -√5×√5×√5×c^3 - 3×√3×√5 abc

(√3 a)^3 - b^3 - (√5c)^3 - 3×√3×√5 abc

now this equation can also be written as

(√3 a)^3 + (-b^3 )+ (- √5c)^3 - 3×(-√3)×(-√5 ) abc

compairing this with , identiry

a^3 +b^3+c^3 - 3abc = ( a+b+c) (a^2+b^2+c^2-ab-bc-ac)


we can factorize our expression as ,

( √3a-b-√5c) ( 3a^2 +b^2+5c^2 +√3ab +√5bc +√15ac)