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Chapter 12: Q. 306 (page 1220)

In the following exercises, expand each binomial using Pascal's Triangle.

(7x+2y)3

Short Answer

Expert verified

The expansion using pascal triangle is(7x+2y)3=343x3+294x2y+84xy2+8y3

Step by step solution

01

Given information

Given binomial expression(7x+2y)3

02

Expand the expression

Expanding, we get

a=7x,b=2yn=3

(7x+2y)3=(7x)3+-(7x)2(2y)1+-(7x)(2y)2+(2y)3

03

Drawing the pascal triangle

The pascal triangle is

04

Picking the coefficients and expanding

Picking the coefficient at the beginning 1,3and then 1,3,3,1

(7x+2y)3=1路(7x)3+3路(7x)2(2y)1+3路(7x)(2y)2+1路(2y)3(7x+2y)3=343x3+294x2y+84xy2+8y3(7x+2y)3=343x3+294x2y+84xy2+8y3

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