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Chapter 12: Q. 12.64 (page 1205)

Use Pascal鈥檚 Triangle to expand(x+1)6

Short Answer

Expert verified

x6+6x5+15x4+20x3+15x2+6x+1

Step by step solution

01

. Given Information

We are given the expression : (x+1)6and we need to solve this using the Pascal's triangle

02

. Pascal's triangle

First we need to expand the given expression by using the formula :

(a+b)n=__an+__an-1b1+__an-1b2+...+__a1bn-1+__bn

After this we find the co-efficient by using the Pascal's triangle , we count the number of expression obtained and then use that number as the row number of the triangle :

03

. Expanding the expression

We need to expand the given expression :

(x+1)6=__x6+__x6-111+__x6-212+__x6-313+__x6-414+__x6-515+__x6-616

(x+1)6=__x6+__x5+__x4+__x3+__x2+__x+__1

04

. Putting the co-efficient

We see that the number of expression obtained after expanding is six so we will take the co-efficient from the sixth row of the Pascal's triangle, so we will get :

x6+6x5+15x4+20x3+15x2+6x+1

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