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Chapter 12: Q. 12.61TI (page 1204)

Use Pascal鈥檚 Triangle to expand(x+y)5

Short Answer

Expert verified

x5+5x4y+10x3y2+10x2y2+5xy4+y5

Step by step solution

01

. Given Information

We are given an expression=(x+y)5to solve it using the Pascal's triangle

02

. Pascal Triangle

The pascal triangle is :

We use this triangle to write the co-efficent of the expression and we explained the expression by using the formula :(a+b)n=an+___an-1b1+___an-2b2+...+___a1bn-1+bn

03

. Expanding the expression 

We expand the expression and we get :

(x+y)5=__x5y0+__x5-1y1+__x5-2y2+__x5-3y3+__x5-4y4+__x5-5y5

(x+y)5=__x5+__x4y+__x3y2+__x2y3+__xy4+__y5

04

. Adding the co-efficient from the Pascal's triangle

After expanding the expression we see that we get 6expression so we will take the sixth row's co-efficient of the pascal triangle. So we get :

x5+5x4y+10x3y2+10x2y2+5xy4+y5

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