Question

Write the coefficient of x2 in the expansion of (x - 2)3

Answer 1

Answer:

The coefficient of x² is -6.

Step-by-step explanation:

The given expression is

$(x-2)^3$

Using the formula:

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

We get

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

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

Therefore, the coefficient of x² is -6.

Answer 2

The coefficient of $(x-2)^{3}=-6$

Given:

Expansion of $(x-2)^{3}$

To find:

The coefficient of $(x-2)^{3}$

Solution:

By formula,$(a-b)^{3}=a^{3}-b^{3}-3 a^{2} b+3 a b^{2}$

Substitute the values of a and b in the above formula, where $a=x, b=2$

$\begin{array}{l}{(x-2)^{3}=x^{3}-2^{3}-3 x^{2}(2)+3 x(2)^{2}} \\ {(x-2)^{3}=x^{3}-8-6 x^{2}+12 x}\end{array}$

To find the coefficient of $x^{2}$,find the term with$x^{2}$in the above equation,  

Therefore, The coefficient of $x^{2}=-6$