Checkpoint: The Binomial Theorem Solution

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Determine the fifth term of the binomial.

${(x - 2)}^{8}$

$r = 5 - 1 = 4 n C r (8, 4) = \frac{8!}{4! (8 - 4)!} = 70 70 {(x)}^{4} {(- 2)}^{4} 70 (16) x^{4} 1, 120 x^{4}$

Note

Q: What will the final term in the expanded binomial expression be?

A: ${(- 2)}^{8}$ or 256

You can use technology or Pascal’s Triangle rather than writing out and simplifying nCr by hand.