Problem 30 Before expanding \((t-4)^{6}\) u... [FREE SOLUTION]

Chapter 15: Problem 30

Before expanding \((t-4)^{6}\) using the binomial theorem, how should the binomial be rewritten?

Short Answer

Expert verified

The given binomial, \((t-4)^6\), should be rewritten in the form of \((x+y)^n\) before expanding using the binomial theorem. To do this, rewrite it as \((t + (-4))^6\), where x = t, y = -4, and n = 6.

Step by step solution

Understand the Binomial Theorem

The Binomial Theorem states that for any natural number n and real number x, y, we have: \[(x + y)^n = \sum_{k=0}^n{n \choose k}x^{n-k}y^k\] where \({n \choose k}\) is the binomial coefficient and can be calculated as: \({n \choose k} = \frac{n!}{k!(n-k)!}\), where "n!" denotes n factorial (the product of all positive integers up to n).

Rewrite the given binomial to fit the Binomial Theorem

In order to rewrite the given binomial, \((t-4)^6\), to fit the Binomial Theorem, we need to express it in the form \((x+y)^n\). We can do this by noting that the expression can be equivalently written as: \[(t + (-4))^6\]

Identify x, y, and n in the rewritten binomial

Now that we rewrote the binomial in the form of \((x+y)^n\), we can identify x, y, and n as follows: - x = t - y = -4 - n = 6 Now the binomial has been rewritten in a form suitable for applying the binomial theorem: \((t + (-4))^6\).

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91影视

Before expanding \((t-4)^{6}\) using the binomial theorem, how should the binomial be rewritten?

Short Answer

Step by step solution

Understand the Binomial Theorem

Rewrite the given binomial to fit the Binomial Theorem

Identify x, y, and n in the rewritten binomial

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