6.8.2 binomial theorem. before we begin find 4 c 0 find 4 c 1 find 4 c 2...

6.8.2 Binomial Theorem

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6.8.2 Binomial Theorem

Before We Begin

Find 4C0 ____________ Find 4C1 ____________ Find 4C2 ____________ Find 4C3 ____________ Find 4C4 ____________

List the 4th Row (Remember that the 4th Row will have a 4 as the second number)

_______________

6.8.2 Binomial Theorem

You can use Combinations to expand binomials. General Formula:

(a+b)n …nCoan + nC1an-1b + nC2an-2b2…

Page 4: 6.8.2 Binomial Theorem. Before We Begin Find 4 C 0 ____________ Find 4 C 1 ____________ Find 4 C 2 ____________ Find 4 C 3 ____________ Find 4 C 4 ____________

Steps to Using Binomial Theorem

Step 1: Set Up Number of Terms (always 1 more than your exponent)

Step 2: Fill in your “nCr” Step 3: Fill in your letters Step 4: Simplify

Page 5: 6.8.2 Binomial Theorem. Before We Begin Find 4 C 0 ____________ Find 4 C 1 ____________ Find 4 C 2 ____________ Find 4 C 3 ____________ Find 4 C 4 ____________

Example 1: Using Binomial Theorem

(g+h)4

_____ + _____ + _____ + _____ + _____

Final Answer: g4 + 4g3h + 6g2h2 + 4gh3 + h4

4C0 4C1 4C2 4C3 4C4g4 g3 g2 g h4h3h2h

Page 6: 6.8.2 Binomial Theorem. Before We Begin Find 4 C 0 ____________ Find 4 C 1 ____________ Find 4 C 2 ____________ Find 4 C 3 ____________ Find 4 C 4 ____________

Example 2: (x-3)5

_____ + _____ + _____ + _____ + _____ + _____

5C05C1 5C2 5C3 5C4 5C5

1x5 5x4 10x3 10x2 5x 1

(-3)55x(-3)410x2(-3)310x3(-3)25x4(-3)1x5

FINAL ANSWER: 1x5 -15x4 +90x3 -270x2 +405x -243

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6.8.2 binomial theorem. before we begin find 4 c 0 ____________ find 4 c 1 ____________ find 4 c 2...

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6.8.2 binomial theorem. before we begin find 4 c 0 find 4 c 1 find 4 c 2...