In Example it was shown that(a + b)5 = a5 + 5a4 b + 10a3b2

Chapter 9, Problem 28E

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Problem 28E

In Example it was shown that

(a + b)5 = a5 + 5a4 b + 10a3b2 + 10a2 b3 + 5ab4 + b35.

Evaluate (a + b)6 by substituting the expression above into the equation

(a + b)6 = (a + b)(a + b)5 and then multiplying out and combining like terms.

Example

Substituting into the Binomial Theorem

Expand the following expressions using the binomial theorem:

$(a\ +\ b){\ }^{5}$

$\left({x\ -\ 4y}\right){\ }^{4}$

Solution

Observe that So let and and substitute into the binomial theorem.

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