Question

If the general term is ^{91}C_{2} x^{89}, what is the expansion?

- (x)
^{91} - (x – 2)
^{90} - (x – 1)
^{91} - (x + 1)
^{90}

^{91}^{90}^{91}^{90}## The correct answer is: (x – 1)^{91}

STEP BY STEP SOLUTION

The general term of an expansion is ^{n}C_{r} x^{n – r} y^{r}.

Clearly, here *n* is 91, and the first term is *x* raised to the power 89.

The second term is raised to power 2.

y^{2} = 1

y = +1 or -1

Therefore, the expansion can either be (x + 1)^{91} or (x – 1)^{91}.

^{n}C

_{r}x

^{n – r}y

^{r}.

*n*is 91, and the first term is

*x*raised to the power 89.

^{2}= 1

^{91}or (x – 1)

^{91}.

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