Question

if (a+3b) =6 , show that a^3 +27b^3+54ab = 216

Answer 1

$a + 3b = 6 \\ {a}^{3} + 27 {b}^{3} + 54ab = 216 \\ \\ {(a + 3b)}^{3} = {6}^{3} = 216 \\ {a}^{3} + 27 {b}^{3} + 9ab(a + 3b) = 216 \\ \\ place \: value \: of \: a + 3b \: here \\ {a}^{3} + 27 {b}^{3} + 9ab(6) = 216 \\ {a}^{3} + 27 {b}^{3} + 54ab= 216 \\ hence \: proved$

Answer 2

It's from which book.....