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 .

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Presentation transcript:

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 ____________ List the 4 th Row (Remember that the 4 th 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 … n C o a n + n C 1 a n-1 b + n C 2 a n-2 b 2 …

Steps to Using Binomial Theorem Step 1: Set Up Number of Terms (always 1 more than your exponent) Step 2: Fill in your “ n C r ” Step 3: Fill in your letters Step 4: Simplify

Example 1: Using Binomial Theorem (g+h) 4 _____ + _____ + _____ + _____ + _____ Final Answer: g 4 + 4g 3 h + 6g 2 h 2 + 4gh 3 + h 4 4C04C04C14C14C24C24C34C34C44C4 g4g4 g3g3 g2g2 gh4h4 h3h3 h2h2 h

Example 2: (x-3) 5 _____ + _____ + _____ + _____ + _____ + _____ 5C05C0 5C15C15C25C25C35C35C45C45C55C5 1x 5 5x 4 10x 3 10x 2 5x1 (-3) 5 5x(-3) 4 10x 2 (-3) 3 10x 3 (-3) 2 5x 4 (-3)1x 5 FINAL ANSWER: 1x 5 -15x 4 +90x x x -243