if x y 3 is expanded what is the sum of the numerical coefficients Free Pre Algebra Algebra Trigonometry Calculus Geometry Statistics and Chemistry calculators step by step
The binomial theorem states that x y n n k 0xkyn k Expand x y 3 Here we are given n 3 and since the binomial starts at k 0 it suffices to say that we are Edited by Wsai12 Jun 9 2021 3 2401 2 I think it s 1 9 18 Another cool trick you can use to find the sum of coefficients is to just plug in c as 1 3 1 1 2 3 1 This
if x y 3 is expanded what is the sum of the numerical coefficients
if x y 3 is expanded what is the sum of the numerical coefficients
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What Is The Sum Of The Infinite Series 1 1 1 2 2 1 3 3
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We can skip n 0 and 1 so next is the third row of pascal s triangle 1 2 1 for n 2 the x 2 term is the rightmost one here so we ll get 1 times the first term to the 0 power times the Answer The expansion of x y 3 is x 3 y 3 3x 2 y 3xy 2 Let us see how to expand x y 3 Explanation The expression x y 3 can be written as x y x y x y First simplify
False True True or False large x 3 y 3 x y x 2 xy y 2 x3 y3 x y x2 xy y2 Challenging Examples What is x y 3 x y 3 x y 3 x y 3 Solution 1 If The coefficient of an algebraic expression 7x 2y 3z 4 7x2y3z4 corresponds to the number that precedes or multiplies the variables in it Numerical coefficients
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Explanation x y 3 x y x y x y Expand the first two brackets x y x y x2 xy xy y2 x2 y2 2xy Multiply the result by the last two brackets This formula is known as the binomial theorem Example 1 Use the binomial theorem to express x y 7 in expanded form Notice the following pattern In general the k th
Example 23 2 2 Determining a specific coefficient in a trinomial expansion Determine the coefficient on x5y2z7 in the expansion of x y z 14 Solution Here we a b 6 a 6 6a 5b 15a 4b 2 20a 3b 3 15a 2b 4 6ab 5 b 6 a b 7 a 7 7a 6b 21a 5b 2 35a 4b 3 35a 3b 4 21a 2b 5 7ab 6 b 7 The
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if x y 3 is expanded what is the sum of the numerical coefficients - Answer The expansion of x y 3 is x 3 y 3 3x 2 y 3xy 2 Let us see how to expand x y 3 Explanation The expression x y 3 can be written as x y x y x y First simplify