Explanation Given information: The expression, ( s + t ) 6 . Formula used: Binomial Theorem: For any positive integer n , ( a + b ) n = n ! n ! ⋅ 0 ! a n + n ! ( n − 1 ) ! ⋅ 1 ! a ( n − 1 ) b + n ! ( n − 2 ) ! ⋅ 2 ! a ( n − 2 ) b 2 + … + n ! 0 ! ⋅ n ! b ( n ) In factorials, 0 ! = 1 Calculation: Consider the formula, ( a + b ) n = n ! n ! ⋅ 0 ! a n + n ! ( n − 1 ) ! ⋅ 1 ! a ( n − 1 ) b + n ! ( n − 2 ) ! ⋅ 2 ! a ( n − 2 ) b 2 + … + n ! 0 ! ⋅ n ! b ( n ) Using this formula in the expansion of ( s + t ) 6 , ( s + t ) 6 = 6 ! 6 ! ⋅ 0 ! s 6 + 6 ! ( 6 − 1 ) ! ⋅ 1 ! s ( 6 − 1 ) t + 6 ! ( 6 − 2 ) ! ⋅ 2 ! s ( 6 − 2 ) t 2 + 6 ! ( 6 − 3 ) ! ⋅ 3 ! ( s ) ( 6 − 3 ) ( t ) 3 + 6 ! ( 6 − 4 ) ! ⋅ 4 ! ( s ) ( 6 − 4 ) ( t ) 4 + 6 ! ( 6 − 5 ) ! ⋅ 5 ! ( s ) ( 6 − 5 ) ( t ) 5 + 6 ! ( 6 − 6 ) ! ⋅ 6 ! ( s ) ( 6 − 6 ) ( t ) 6 = 6 ! 6 ! ⋅ 0 !

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ISBN: 9781260962024

Author: Miller

Publisher: MCG

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Chapter 14.1, Problem 39PE

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To calculate: The expansion of (s+t)6 using binomial theorem.

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Chapter 14.1, Problem 38PE

Chapter 14.1, Problem 40PE

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Chapter 14 Solutions

ALEKS 360 ONLINE ACCESS (6 WEEKS) FOR B

Ch. 14.1 - Prob. 1SP Ch. 14.1 - Prob. 2SP Ch. 14.1 - Evaluate the expressions. 3. 1! Ch. 14.1 - Prob. 4SP Ch. 14.1 - Prob. 5SP Ch. 14.1 - Prob. 6SP Ch. 14.1 - Write out the first three terms of ( x + y ) 5 .Ch. 14.1 - 8. Use the binomial theorem to expand . Ch. 14.1 - Use the binomial theorem to expand ( 2 a − 3 b 2 )...Ch. 14.1 - Find the fourth term of ( x + y ) 8 .

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The expansion of ( s + t ) 6 using binomial theorem.

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Chapter 14 Solutions