Question 925477
Use Pascal's Triangle to expand each binomial.
{{{(x + y)^8}}}

ANSWER:

Pascal's Triangle. 

It is a triangle of numbers,  which is given below:


1
1 1
1 2 1
1 3 3 1
1 4 6 4 1
1 5 10 10 5 1
1 6 15 20 15 6 1
1 7 21 35 35 21 7 1
1 8 28 56 70 56 28 8 1
1 9 36 84 126 126 84 36 9 1
1 10 45 120 210 252 210 120 45 10 1


Each number in the triangle is the sum of two above. For example, the 6 on line 5 is the sum of the pair of 3's above. So the next line is

1, 10 (1 + 9), 45 (9 + 36), 120 (36 + 84), etc.


Study these numbers and see if you can figure what the next line should be before reading on . . .

Your question.


{{{(x+y)^8}}}

Nineth raw of the triangle gives,COEFFIECIENTS OF THE EXPANSION.

That is, 
{{{1}}}{{{ 8}}}{{{ 28}}}{{{ 56}}}{{{ 70}}}{{{ 56}}}{{{ 28}}}{{{ 8}}}{{{ 1}}}

And the variable terms  will come like this,

{{{x^8}}}

{{{x^7 * y^1}}}

{{{x^6* y^2}}}

{{{x^5 * y^3}}}

{{{x^4 * y^4}}}

{{{x^3 * y^5}}}

{{{x^2*x^6}}}

{{{x^1*x^7}}}

{{{y^8}}]

(power of the first term will decrease while power of second term will increase till it is {{{8}}})

Since here it is {{{(x + y)}}}, the sign of the all  terms will be   positive,


{{{(x + y)^8=   1x^8+ 8x^7*y^1+ 28x^6*y^2+56x^5*y^3+ 70x^4*y^4+ 56x^3*y^5+ 28x^2*y^6+8x*y^7+y^8}}}


{{{(x + y)^8=  x^8+8x^7*y+28x^6*y^2+56x^5*y^3+70x^4*y^4+56x^3*y^5+28x^2*y^6+8x* y^7+y^8}}}

which is the  answer to your question