Q. 302 In the following exercises, expa... [FREE SOLUTION]

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Intermediate Algebra

OPENSTAX

$Math Studyset 91影视 Explanations$ Math

OER 2017 Edition 路 1346 pages

ISBN: 9780998625720

Chapter 11: Q. 302 (page 1069)

In the following exercises, expand each binomial using Pascal's Triangle.
$(a + b)^{7}$

Short Answer

Expert verified

The expansion using pascal triangle is $(a + b)^{7} = a^{7} + 7 a^{6} b + 21 a^{5} b^{2} + 35 a^{4} b^{3} + 35 a^{3} b^{4} + 21 a^{2} b^{5} + 7 a b^{6} + b^{7}$

Step by step solution

Given information

Given the binomial expression ${(a + b)}^{7}$

Expand the expression

Expanding, we get

$a = a, b = b n = 7$

$(a + b)^{7} = a^{7} +_{-} a^{6} (b)^{1} +_{-} a^{5} (b)^{2} +_{-} a^{4} (b)^{3} +_{-} a^{3} (b)^{4} + a^{2} (b)^{5} + a (b)^{6} + b^{7}$

Drawing the Pascal triangle

The Pascal triangle is

Expanding using pascal triangle

Picking the coefficients from the row of the Pascal triangle, we get

$(a + b)^{7} = 1 路 a^{7} + 7 路 a^{6} (b)^{1} + 21 路 a^{5} (b)^{2} + 35 路 a^{4} (b)^{3} + 35 路 a^{3} (b)^{4} + 21 路 a^{2} (b)^{5} + 7 路 a (b)^{6} + 1 路 (b)^{7} {(a + b)}^{7} = = a^{7} + 7 a^{6} b + 21 a^{5} b^{2} + 35 a^{4} b^{3} + 35 a^{3} b^{4} + 21 a^{2} b^{5} + 7 a b^{6} + b^{7} {(a + b)}^{7} = a^{7} + 7 a^{6} b + 21 a^{5} b^{2} + 35 a^{4} b^{3} + 35 a^{3} b^{4} + 21 a^{2} b^{5} + 7 a b^{6} + b^{7}$

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91影视

In the following exercises, expand each binomial using Pascal's Triangle.
$(a + b)^{7}$

Short Answer

Step by step solution

Given information

Expand the expression

Drawing the Pascal triangle

Expanding using pascal triangle

One App. One Place for Learning.

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91影视

In the following exercises, expand each binomial using Pascal's Triangle.(a+b)7

Short Answer

Step by step solution

Given information

Expand the expression

Drawing the Pascal triangle

Expanding using pascal triangle

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Calculus

Logic and Functions

Geometry

Applied Mathematics

Discrete Mathematics

Decision Maths

Study anywhere. Anytime. Across all devices.

In the following exercises, expand each binomial using Pascal's Triangle.
$(a + b)^{7}$