Pearson Algebra 2 Common Core, 2011
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Pearson Algebra 2 Common Core, 2011 View details
Cumulative Standards Review

Exercise 25 Page 760

To find the coefficient of the term of the binomial expansion, we should recall the Binomial Theorem. It states that for every positive integer we can expand the expression by using the numbers in the row of Pascal's Triangle.
In the above formula, are the numbers in the row of Pascal's Triangle.

It can be shown that the coefficient of the row of the Pascal's Triangle equals Therefore, we can restate the binomial theorem using combinations.

Next, let's recall the formula to calculate the combination
We will use this to substitute the values of the combinations in the formula for the binomial expansion.
Finally, let's simplify the expression.
Simplify
The coefficient of the term is equal to

Showing Our Work

Calculating
As previously mentioned, there is a formula to calculate the value of
Let's calculate using this formula.

We found that By following the same procedure, the values of the other combinations can be calculated.