Question

Factorise 8a^3+b^3+12a^2b+6ab^2

Answer 1

8a3 + b3 + 12a2b + 6ab2
SOL: 8a3 + b3 + 12a2b + 6ab2
= (2a)3 + (b)3 + 12a2b + 6ab2
= (2a)3 + (b)3 + 6ab (2a + b)
= (2a)3 + (b)3 + 3(2a)(b) (2a + b)
BY USING (x + y)3 = x3 + y3 + 3xy(x + y)
Putting x = 2a, y = b
= (2a + b)3
= (2a + b) (2a + b) (2a + b)

Answer 2

The answer to the factorisation is, (2a+b) (2a+b) (2a+b)

Given : The given algebraic expression is, 8a^3+b^3+12a^2b+6ab^2

To find : The factorisation of the given algebraic expression.

Solution :

We can simply solve this mathematical problem by using the following mathematical process. (our goal is to factorise the given algebraic expression)

Here, we will be using general algebraic formula.

Actual algebraic expression = 8a³+b³+12a²b+6ab²

So,

= 8a³+b³+12a²b+6ab²

= 8a³+12a²b+6ab²+b³

= (2a)³ + [3 × (2a)² × b] + [3 × 2a × (b)²] + (b)³

= (2a+b)³

= (2a+b) (2a+b) (2a+b)

(This cannot be further factorised. That's why this will be considered as the final result.)

Used formula :

• (a+b)³ = a³+3a²b+3ab²+b³

Hence, the answer to the factorisation is, (2a+b) (2a+b) (2a+b)