Question

Write the coefficient of x square in the expansion of x - 2 cube

Answer 1

Answer:

$Coefficient \: of \: x^{2}\:in \\the \: expansion \:of \:(x-2)^{3}=-6$

Step-by-step explanation:

$Expansion \: of \:(x-2)^{3}\\=x^{3}-3\times x^{2}\times 2+3\times x\times 2^{2}-2^{3}$

/* By algebraic identity:

(a-b)³ = a³-3a²b+3ab²-b³ */

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

$Now, Coefficient \:of \:x^{2}\\= The \: number \: multiplied\:with \:x^{2}\\=-6$

Therefore,

$Coefficient \: of \: x^{2}\:in \\the \: expansion \:of \:(x-2)^{3}=-6$

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Answer 2

Step-by-step explanation:

Coefficientofx

2

in

theexpansionof(x−2)

3

=−6

Step-by-step explanation:

\begin{gathered}Expansion \: of \:(x-2)^{3}\\=x^{3}-3\times x^{2}\times 2+3\times x\times 2^{2}-2^{3}\end{gathered}

Expansionof(x−2)

3

=x

3

−3×x

2

×2+3×x×2

2

−2

3

/* By algebraic identity:

(a-b)³ = a³-3a²b+3ab²-b³ */

=x^{3}-6x^{2}+12x-8=x

3

−6x

2

+12x−8

\begin{gathered}Now, Coefficient \:of \:x^{2}\\= The \: number \: multiplied\:with \:x^{2}\\=-6\end{gathered}

Now,Coefficientofx

2

=Thenumbermultipliedwithx

2

=−6