Binomial Theorem

Fill in all the gaps, then press "Check" to check your answers. Use the "Hint" button to get a free letter if an answer is giving you trouble. You can also click on the "[?]" button to get a clue. Note that you will lose points if you ask for hints or clues!

1. An expression consisting of two terms, connected by positive or negative sign is called expression.
2. The total number of terms in the binomial expansion of

{(a + b)}^{n}

is .
3. The coefficients of terms equidistant from the beginning and the end are .
4. If n is , then in the expansion of

{(a + b)}^{n}

, the middle term is

{(\frac{n}{2} + 1)}^{t h}

term.
5. If n is , then in the expansion of

{(a + b)}^{n}

, the middle terms are

{(\frac{n + 1}{2})}^{t h}

term and

{(\frac{n + 3}{2})}^{t h}

term.
6. The coefficients of the expansions are arranged in an .
7. The number of terms in the expansion of

{(1 - 3 x + 3 x^{2} - x^{3})}^{8}

is .
8. The middle term in the expansion of

{(\frac{2 x^{2}}{3} + \frac{3}{2 x^{2}})}^{10}

is .
9. If in the expansion of

{(1 + x)}^{20}

, the coefficients of

r^{t h}

and

{(r + 4)}^{t h}

terms are equal, then r is equal to .
10. If in the expansion of

{(a + b)}^{n}

and

{(a + b)}^{n + 3}

, the ratio of the coefficients of second and third terms, and third and fourth terms respectively are equal, then n is .

Binomial Theorem

Gap-fill exercise