Question

factorize 27a cube + 125b cube​

Answer 1

Answer:

see the attached document for the steps

Answer 2

Answer:

Factorize 27a³+ 125b³​

$27a^{3}+ 125b^{3}\\(3a)^{3} + (5b)^{3}\\\\a^{3} +b^{3} = (a+b) (a+b)^{2}\\apply\ this\ identity\\\\(3a)^{3} + (5b)^{3} = (3a+5b) (3a+5b)^{2} (Here\ a\ is\ 3a\ and\ b\ is\ 5b)\\(3a+5b)^{2} = (3a)^{2} + 2(3a)(5b) + (5b)^{2} (because\ (a+b)^{2} = a^{2} + 2ab +b^{2} )\\(3a+5b)^{2} = 9a^{2} + 30ab + 25b^{2}\\\\so:\ \\a^{3} +b^{3} = (a+b) (a+b)^{2} = (a+b) (9a^{2} + 30ab + 25b^{2})\\(a+b) (9a^{2} + 30ab + 25b^{2}) = a(9a^{2} + 30ab + 25b^{2}) + b(9a^{2} + 30ab + 25b^{2})$$(a+b) (9a^{2} + 30ab + 25b^{2}) = 9a^{3} + 30a^{2} +25ab^{2} + 9a^{2}b+30ab^{2}+25b^{3}\\(a+b) (9a^{2} + 30ab + 25b^{2}) = 9a^{3}+25b^{3}+9a^{2}b+25ab^{2}+30ab^{2}\\(a+b) (9a^{2} + 30ab + 25b^{2}) = 9a^{3}+25b^{3}+9a^{2}b+55ab^{2}\\\\Hence\ 27a^{3} + 125b^{3}= 9a^{3}+25b^{3}+9a^{2}b+55ab^{2}$​

(Please mark my answer brainliest if it has helped you)