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**Unformatted text preview: **(Chapter 9: Discrete Math) 9.32 PART C: EXPANDING POWERS OF GENERAL BINOMIALS Example Expand and simplify 3 x − y ( ) 3 using the Binomial Theorem. Solution We will use the template for a + b ⎡ ⎣ ⎤ ⎦ 3 . 3 x − y ( ) 3 = 3 x Sub a = 3 x + − y ( ) Sub b = − y ⎡ ⎣ ⎢ ⎢ ⎢ ⎢ ⎢ ⎤ ⎦ ⎥ ⎥ ⎥ ⎥ ⎥ 3 = a + b [ ] 3 = a 3 + 3 a 2 b + 3 ab 2 + b 3 Sub back: a ← 3 x ( ) , b ← − y ( ) = 3 x ( ) 3 + 3 3 x ( ) 2 − y ( ) + 3 3 x ( ) − y ( ) 2 + − y ( ) 3 Simplify. First, do powers. = 27 x 3 + 3 9 x 2 ( ) − y ( ) + 3 3 x ( ) y 2 ( ) − y 3 = 27 x 3 − 27 x 2 y + 9 xy 2 − y 3...

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