Question

Expand the following using the binomial theorem and Pascal's triangle.
(x + 2)6

Answer 1

1
121
1331
so on

Answer 2

x^6 must be the first term

Answer 3

really finish the triangle to the 6th row what do you get?

Answer 4

I don't understand.
The triangle is
1
121
1331?

Answer 5

okay well the triangle is jjust a tool to quickly solve this problem

Answer 6

i strongly suggest to google a explanation of the triangle, as this will save you hundreds of hours.

Answer 7

So, I would expand the triangle to the 6th row because (x+2) is raised to the 6th?

Answer 8

I understand how to get the triangle now, thank you. But how do I solve it?

Answer 9

1
1 2 1
1 3 3 1
1 4 6 4 1
1 5 10 5 1
1 6 15 20 6 1

Answer 10

the sixth row will be the coefficients

Answer 11

Ah ok

Answer 12

So
(1x+2)
(6x+2)
ect?

Answer 13

so for example so that I don't answer the question for you ill do (x+2)^5

Answer 14

actually ill do (x+y)^5

Answer 15

x^5+x^4y+x^3y^2+x^2y3+xy^4+y^5

Answer 16

that's the answer to my example^^^

Answer 17

thats without the constants inforont of variables.

Answer 18

I only showed how to do the coefficients

Answer 19

x^5+5x^4y+10x^3y^2+10x^2y3+5xy^4+y^5 is the full answere

Answer 20

Ok
So I would do
x^6+12x^5+60x^4+160x^3+240^2+192x+64?

Answer 21

I think you did it right but look at your triangle its wrong 5th row should have extra 10

Answer 22

this then messes up your 6th row

Answer 23

Oh ok!

Answer 24

the triangle method is never required to do, but just know that later in your math career its probably best for you to rememorize it and utilize it, as it can save you tons of time.