Question

factorise32a^3+108b^3​

Answer 1

Answer:

$32 {a}^{3} + 108 {b}^{3} \\ = 4(8{a}^{3} + 27{b}^{3}) \\ = 4((2{a})^{3} + (3{b})^{3}) \\ = 4(( {2a + 3b})^{3} - 3 \times 2a \times 3b(2a + 3b) )\\ = 4( ({2a + 3b})^{3} - 18 ab(2a + 3b) )\\ = 4(2a + 3b)({( {2a + 3b)}^{2} - 18ab}) \\ = 4(2a + 3b) (4 {a}^{2} + 9 {b}^{2} + 12ab- 18ab) \\ = 4(2a + 3b)(4{a}^{2} + 9 {b}^{2} - 6ab)$