Question

Factorise each of the following :
(a) 8a³+b³+12a²b+6ab²​

Answer 1

Formula :

${a}^{3} + {b}^{3} + 3ab(a + b).$

Solution :

${8a}^{3} + {b}^{3} + 12 {a}^{2}b + 6a {b}^{2} \\ \\ {(2a)}^{3} + ({b})^{3} + 3 \times 2a \times b \times (2a + b) \\ \\ ( {2a + b})^{3} .$

Answer 2

$[{a}^{3} + {b}^{3} + 3ab(a + b)].\\ \\ \\\begin{gathered}{8a}^{3} + {b}^{3} + 12 {a}^{2}b + 6a {b}^{2} \\ \\ {(2a)}^{3} + ({b})^{3} + 3 \times 2a \times b \times (2a + b) \\ \\ ( {2a + b})^{3} .\end{gathered}$