Factorise
Question 1. x^3+27
Solution:-
we have x³+27
=(x)³+3³
= (x+3) (x²-3x+3²) ,since [a³+b³=(a+b) (a²-ab+b²)]
=(x+3) (x²-3x+9)
Question 2. 27a^3+64b^3
Solution:-
we have 27a³+64b³
=(3a)³+(4b)³
= (3a+4b) {(3a)²-3a×4b+(4b)²) , since [a³+b³=(a+b) (a²-ab+b²)]
=(3a+4b) (9a²-12ab+16b²)
Question 3. 125a^3+1/8
Solution:-
we have 125a³+1/8
=(5a)³+(1/2)³
= {5a+(1/8)} {(5a)²-5a×(1/2)+(1/2)²) , since [a³+b³=(a+b) (a²-ab+b²)]
={5a+(1/8)} {25a²-(5a/2)+(1/4)}
Question 4. 216x^3+(1/125)
Solution:-
we have 216x³+(1/125)
=(6x)³+(1/5)³
= {6x+(1/5)} {(6x)²-6x×(1/5)+(1/5)²) , since [a³+b³=(a+b) (a²-ab+b²)]
={6x+(1/5)} {36x²-(6x/5)+(1/25)}
