Question

$if \: 2a - 3b = 3 \: and \: ab = 2 \: find \: the \: value \: of \: 8a {}^{3} - 27b ^{3}$
Mathematics : Expansions ​

Answer 1

Answer:

Note :-

${(x - y)}^{3} = {x}^{3} - {y}^{3} - 3xy(x - y)$

${(2a - 3b)}^{3} = {8a}^{3} - {27b}^{3} - 18ab(a - b)$

Substituting the values given ,

${3}^{3} = {8a}^{3} - {27b}^{3} - 3(2)(3)$

${8a}^{3} - {27b}^{3} = 27 + 18$

${8a}^{3} - {27b}^{3} = 45$