Question

Which of the following is the correct expansion of the binomial (x + y)6?



x6 + 6x5y + 15x4y2 + 20x3y3 + 15x2y4 + 6xy5 + y6



x6 + 155y + 6x4y2 + 20x3y3 + 6x2y4 + 15xy5 + y6



x6 + 6x5y5 + 15x4y4 + 20x3y3 + 15x2y2 + 6xy1 + y6



x6 + 6x5y + 20x4y2 + 15x3y3 + 20x2y4 + 6xy5 + y6

Answer 1

Do you remember the binomial expansion?

Answer 2

And do you know the Pascal triangle?

Answer 3

uh no i dont

Answer 4

like i know it but i don't remember it

Answer 5

Ok. The binomial expansion tell you this, for example, for the the 2 and 3 powers,
\[(x+y)^2=x^2+2xy+y^2\]
\[(x+y)^3=x^3+3x^2y+3xy^2+y^3\]

Answer 6

what

Answer 7

Do you see how it goes?

Answer 8

no :(

Answer 9

You can do the same thing with the sixth power,
\[(x+y)^6=x^6+6x^5y+15x^4y^2+20x^3y^3+15x^2y^4+6xy^5+y^6\]

Answer 10

The way to obtain this is just to multply, as @BPDlkeme567 says,
\[(x+y)(x+y)(x+y)(x+y)(x+y)(x+y)\]

Answer 11

can you not multiply (x + y)(x+y)?

Answer 12

no ;-;

Answer 13

Okay so we need to start there

Answer 14

c:

Answer 15

Yes, it is better the way @BPDlkeme567 says.

Answer 16

that is known as the difference of two squares. i.e x^2 + y^2

Answer 17

so, (x + y)(x- -y) = x^2 + y^2

Answer 18

hey human calculator @John_ES , can you take over and teach binomial theorem?

Answer 19

and polynomial identities

Answer 20

@tinalikescats it is actually based on a very simple idea, invented by the chines (forget that people call it Pascal's triangle), but have a look on wikipedia at Pascal's triangle.

Answer 21

wot

Answer 22

Pascals triangle starts with 1, next two numbers must be put below this, which is the sum of the previous numbers, but since there is only 1 previous number the two numbers under this are 1

Answer 23

oh, sorry, this might seem irrelevant, but these are the co-efficients of the mathematical expressions

Answer 24

are you there?

Answer 25

x6 + 6x5y + 15x4y2 + 20x3y3 + 15x2y4 + 6xy5 + y6