Chapter 12: Q. 219 (page 1213)

In the following exercises, expand each binomial ${(y - 3)}^{4}$ .

Short Answer

Expert verified

The Binomial expansion is $y^{4} - 12 y^{3} + 54 y^{2} - 108 y + 81$ .

Step by step solution

Step 1. Given Information.

The expression is ${(y - 3)}^{4}$ .

Step 2. Apply Binomial Theorem

Binomial Theorem is :- ${(a + b)}^{n} = \sum_{i = 0}^{n} (\binom{n}{i}) a^{(n - i)} b^{i}$

Step 3. Solve for Binomial Theorem .

Using Binomial Theorem , we get:-

$\sum_{i = 0}^{4} (\binom{4}{i}) y^{(4 - i)} {(- 3)}^{i}$

Expanding :-

$\frac{4!}{0! (4 - 0)!} y^{4} {(- 3)}^{0} + \frac{4!}{1! (4 - 1)!} y^{3} {(- 3)}^{1} + \frac{4!}{2! (4 - 2)!} y^{2} {(- 3)}^{2} + \frac{4!}{3! (4 - 3)!} y {}^{1}{(- 3)}^{3} + \frac{4!}{4! (4 - 4)!} y^{0} {(- 3)}^{4}$

Simplifying the terms ,we get:-

$y^{4} - 12 y^{3} + 54 y^{2} - 108 y + 81$

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In the following exercises, expand each binomial ${(y - 3)}^{4}$ .

Short Answer

Step by step solution

Step 1. Given Information.

Step 2. Apply Binomial Theorem

Step 3. Solve for Binomial Theorem .

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Step by step solution

Step 1. Given Information.

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One App. One Place for Learning.

Most popular questions from this chapter

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In the following exercises, expand each binomial ${(y - 3)}^{4}$ .