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Chapter 12: Q. 12.63 (page 1205)

Use Pascal鈥檚 Triangle to expand (x+2)4

Short Answer

Expert verified

x4+8x3+24x2+32x2+16

Step by step solution

01

. Given Information

We are given the expression :

(x+2)4and 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-2b2+...+__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+2)4=__x4+__x4-121+__x4-222+__x4-323+__+x4-424

(x+2)4=__x4+__2x3+__4x2+__8x3+__16

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 :

x4+4.2x3+6.4x2+4.8x+16=x4+8x3+24x2+32x+16

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