Question

Factorise 27a³+36a²b+12ab²

Answer 1

Answer:

27a³+8b³-18a²b-12ab²

=(3a)³+(2b)²-(3a)²*2b-3a*(2b)²

Answer 2

27a³ + 36a²b + 12ab² = 3a(3a + 2b)(3a + 2b)

Given :

The expression 27a³ + 36a²b + 12ab²

To find :

To factorise the expression

Solution :

Step 1 of 2 :

Write down the given expression

The given expression is

27a³ + 36a²b + 12ab²

Step 2 of 2 :

Factorise the expression

$\sf 27 {a}^{ 3} + 36 {a}^{2} b + 12a {b}^{2}$

$\sf = 3a(9 {a}^{ 2} + 12a b + 4 {b}^{2} )$

$\sf = 3a \bigg[ \: {(3a)}^{ 2} + 2 \times 3a \times 2b + {(2b)}^{2} \bigg]$

$\sf = 3a {(3a + 2b)}^{ 2}$

$\sf = 3a (3a + 2b)(3a + 2b)$

Thus we get ,

27a³ + 36a²b + 12ab² = 3a(3a + 2b)(3a + 2b)