Question

How many terms are in the expansion (x + y)10.

10

13

12

11


I choose 10

Answer 1

The question is \(\sf (x+y)^{10}\) right?

Answer 2

@TheSmartOne yes

Answer 3

It might help to look at smaller expansions

\[\Large (x+y)^2 = x^2+2xy+y^2 \ \rightarrow \ \text{3 terms}\]
\[\Large (x+y)^3 = x^3+3x^2y+3xy^2+y^3 \ \rightarrow \ \text{4 terms}\]

and see what pattern you can find

Answer 4

^^

Answer 5

After seeing what Jim posted, what do you think the correct answer will be? :)

Answer 6

10.

Answer 7

You didn't fully understand what Jim posted...

\(\sf \Large (x+y)^\color{red}{2} \to \color{red}{3}~ terms\)
\(\sf \Large (x+y)^\color{red}{3} \to \color{red}{4}~ terms\)
\(\sf \Large (x+y)^\color{red}{4} \to \color{red}{5}~ terms\)
\(\sf \Large (x+y)^\color{red}{5} \to \color{red}{6}~ terms\)
\(\sf \Large (x+y)^\color{red}{6} \to \color{red}{7}~ terms\)
...

Answer 8

(x+y)^10 is 10 terms

Answer 9

@TheSmartOne is basically saying that for any nonnegative integer n

\[\Large (x+y)^n \rightarrow \text{n+1 terms}\]

Answer 10

for instance, if n = 1, then

\[\Large (x+y)^n \rightarrow \text{n+1 terms}\]
\[\Large (x+y)^1 \rightarrow \text{1+1 terms}\]
\[\Large (x+y)^1 = x+y \rightarrow \text{2 terms}\]

Answer 11

that has been our whole point, so that way you would revise your answer. :)

Answer 12

thank yu

Answer 13

jim also

Answer 14

no problem

Answer 15

you're welcome