Question

by using standard formula explain this (2x -1) ^3 ​

Answer 1

$( {2x - 1)}^{3}$

$( {2x)}^{3} - ( {1)}^{3} - 3 \times 2x \times 1(2x - 1)$

$8 {x}^{3} - 1 - 6x(2x - 1)$

$8 {x}^{3} - 1 - 12 {x}^{2} + 6x$

Answer 2

Given:

$(2x - 1)^3$

To Find:

$\text{Explain}$

First, we know that this is how the formula is derived:

$(a - b)^3 = (a - b)(a - b)^2$

$(a - b)^3 = (a - b)(a^2 + b^2 - 2ab)$

$(a - b)^3 = a^3 + ab^2 - 2a^2b - a^2b - b^3 + 2ab^2$

$(a - b)^3 = a^3 - b^3 - 3a^2b + 3ab^2$

$(a - b)^3 = a^3 - b^3 - 3ab( a - b)$

Applying the formula to the question:

$(a - b)^3 = a^3 - b^3 - 3ab( a - b)$

$(2x - 1)^3 = (2x)^3 - (1)^3 - 3(2x)(1)( 2x - 1)$

$(2x - 1)^3 = 8x^3 - 1 - 6x( 2x - 1)$

$(2x - 1)^3 = 8x^3 - 1 - 12x^2 + 6x$

$(2x - 1)^3 = 8x^3 - 12x^2 + 6x - 1$

$\boxed {\boxed {\text{Answer : }(2x - 1)^3 = 8x^3 - 12x^2 + 6x - 1 }}$