Question

How to solve (2x + 1) 3 by using identity?

Answer 1

Question :-

→  (2x + 1)³

Solution :-

→  (2x)³ + (1)³ + 3(2x)(1) (2x+1)

→  8x³ + 1 + 6x(2x+1)

→  8x³ + 1 + 12x² + 6x

→  8x³ + 12x² + 6x + 1

Identity used :-

→  (a + b)³ = a³ + b³ + 3ab(a+b)

Where,

a = 2x, b = 1

Answer 2

QUESTION :- Solve $\sf {(2x + 1)}^{3}$ using suitable identity.

SOLUTION :-

Using identity,

$\sf \star \fbox \green{{(a + b)}^{3} = {x}^{3} + {y}^{3} + 3ab(a + b)}$

Here a = $\sf 2x$ and b = $\sf 1$

$\sf {(2x + 1)}^{3}$

$\sf →{(2x)}^{3} + {1}^{3} + 3(2x)(1)(2x + 1)$

$\sf → {8x}^{3} + 1 + 6x(2x + 1)$

$\sf \blue{→ {8x}^{3} + {12x}^{2} + 6x + 1}$

Hence $\sf {(2x + 1)}^{3}$ is equal to $\sf {8x}^{3} + {12x}^{2} + 6x + 1$.