Question Find The Coefficient Of X^2y^3z^3 In The Expansion Of (xyz)^8 (121) This problem has been solved!Click here👆to get an answer to your question ️ If x y z = 12 and x^2 y^2 z^2 = 96 and 1x 1y 1z = 36 then the value of x^3 y^3 z^3 isSteps for Solving Linear Equation x2y3z = 2 x 2 y 3 z = 2 Subtract x from both sides Subtract x from both sides 2y3z=2x 2 y 3 z = 2 − x Subtract 3z from both sides Subtract 3 z
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Expand x minus 2 y - 3 z whole square-Expand (− 2 x 5 y − 3 z) 2 using suitable identities Hard Answer (− 2 x 5 y − 3 z) 2 is of the form (a b c) 2 (a b c) 2 = a 2 b 2 c 2 2 a b 2 b c 2 c a where a = − 2 x, b = 5 y, c = − 3 z ∴ (− 2 x 5 y − 3 z) 2 = 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 (x2 y2 −2xy)(x − y) = x3 − x2y xy2 − y3 −2x2y 2xy2 ⇒ x3 −y3 − 3x2y 3xy2 Always expand each term in the bracket by all the other
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Taylor series and Maclaurin series LinksTaylor reminder theorem log(11)≈01 ((01)^2/2)((01)^3/3) Find minimum error and exact value https//youtube⋅(x)3−k ⋅(y)k ∑ k = 0 3 3 3 3 logxy logxlogy = Use property 3 to rewrite the multiplication as addition 3 3 = 2logx7logy Use Property 5 to move the exponents out front Thus, ( ) 27 3 3 3 logxy 2logx7logy = Example 2 Use the properties of logarithms to expand 8 3 x log y æ ö ç ÷ ç ÷ Ł ł 1 2 8 8 3 3 x x
(x y) 7 = x 7 7x 6 y 21x 5 y 2 35x 4 y 3 35x 3 y 4 21x 2 y 5 7xy 6 y 7 When the terms of the binomial have coefficient(s), be sure to apply the exponents to these coefficients Example Write out the expansion of (2 x 3 y ) 4To ask Unlimited Maths doubts download Doubtnut from https//googl/9WZjCW Find the coefficient of `x^2 y^3 z^4` in the expansion of ` (axbycz)^9`(xyz)^3 (x y z) (x y z) (x y z) We multiply using the FOIL Method x * x = x^2 x * y = xy x * z = xz y * x = xy
For this question, you can use the Multinomial Theorem (a version of the Binomial Theorem for three or more terms) Or, you can group the terms (as in, ((xy) z) n) and apply the Binomial Theorem as usualExpand Using the Binomial Theorem (xyz)^3 (x y z)3 ( x y z) 3 Use the binomial expansion theorem to find each term The binomial theorem states (ab)n = n ∑ k=0nCk⋅(an−kbk) ( a b) n = ∑ k = 0 n n C k ⋅ ( a n k b k) 3 ∑ k=0 3!Expand ( X Y Z )2 CISCE ICSE Class 9 Question Papers 10 Textbook Solutions Important Solutions 5 Question Bank Solutions Concept Notes & Videos 258 Syllabus Advertisement Remove all ads Expand ( X Y Z )2 Mathematics
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Compute answers using Wolfram's breakthrough technology & knowledgebase, relied on by millions of students & professionalsClick here👆to get an answer to your question ️ Using the identity and proof x^3 y^3 z^3 3xyz = (x y z)(x^2 y^2 z^2 xy yz zx)Expand 1/12*((xyz)^6 2(x^6y^6z^6) 2(x^3y^3z^3)^2 4(x^2y^2z^2)^3 3(xyz)^2(x^2y^2z^2)^2) Extended Keyboard;
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Compute answers using Wolfram's breakthrough technology & knowledgebase, relied on by millions of students & professionals For math, science, nutrition, history8 E(X Y) = E(X) E(Y) (The expectation of a sum = the sum of the expectations This rule extends as you would expect it to when there are more than 2 random variables, eg E(X Y Z) = E(X) E(Y) E(Z)) 9 If X and Y are independent, E(XY) = E(X)E(Y) (This rule extends as you would expect it to for more than 2 randomStack Exchange network consists of 177 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers Visit Stack Exchange
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Expandcalculator en Related Symbolab blog posts Middle School Math Solutions – Equation Calculator Welcome to our new "Getting Started" math solutions series Over the next few weeks, we'll be showing how Symbolab (xy)^4 = x^4y^4z^44x^3y4xy^34y^3z4yz^34z^3x4zx^36x^2y^26y^2z^26z^2x^212x^2yz12xy^2z12xyz^2 Note that (ab)^4 = a^44a^3b6a^2b^24ab^3b^4 So we can find the terms of (xyz)^4 that only involve 2 of x, y, z by combining the expansions of binomial powers, One way to see that is to think about setting each of x, y, z (xy)^3 (yz)3 (zx)^3 = 3(xy)(yz)(zx) That is it no constraints etc It mentions "This can be done by expanding out the brackets, but there is a more elegant solution" Homework Equations The Attempt at a Solution First of all this only seems to hold in special cases as I have substituted random values for x,y and z and they do not agree
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The calculator allows you to expand and collapse an expression online , to achieve this, the calculator combines the functions collapse and expand For example it is possible to expand and reduce the expression following ( 3 x 1) ( 2 x 4), The calculator will returns the expression in two forms expanded and reduced expression 4 14 ⋅ x3D Transformation MCQ Questions And Answers 3D Transformation MCQs This section focuses on "3D Transformation" in Computer Graphics These Multiple Choice Questions (MCQ) should be practiced to improve the Computer Graphics skills required for various interviews (campus interview, walkin interview, company interview), placements, entrance exams and other x^33x^23x1 "note that" (xa)^3=x^3(aaa)x^2(aaaaaa)xa^3 (x1)^3toa=1 rArr(x1)^3=x^3(111)x^2(111)x(1)^3 =x^33x^23x1
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Free math problem solver answers your algebra, geometry, trigonometry, calculus, and statistics homework questions with stepbystep explanations, just like a math tutorRewrite (x−y −z)2 ( x y z) 2 as (x−y−z)(x−y−z) ( x y z) ( x y z) Expand (x−y−z)(x−y−z) ( x y z) ( x y z) by multiplying each term in the first expression by each term in the second expression Simplify each term Tap for more steps Multiply x x by x xIn elementary algebra, the binomial theorem (or binomial expansion) describes the algebraic expansion of powers of a binomialAccording to the theorem, it is possible to expand the polynomial (x y) n into a sum involving terms of the form ax b y c, where the exponents b and c are nonnegative integers with b c = n, and the coefficient a of each term is a specific positive
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Simplify (xyz)(xyz) Expand by multiplying each term in the first expression by each term in the second expression Simplify terms Tap for more steps Combine the opposite terms in Tap for more steps Reorder the factors in the terms and Add andWolframAlpha Computational Intelligence Enter what you want to calculate or know about Extended Keyboard Examples Compute expertlevel answers using Wolfram's breakthrough algorithms, knowledgebase and AI technologyAnswer by lenny460 (1073) ( Show Source ) You can put this solution on YOUR website!
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Start your free trial In partnership with You are being redirected to Course Hero I want to submit the same problem to Course Hero CancelOur online expert tutors can answer this problem Get stepbystep solutions from expert tutors as fast as 1530 minutes Your first 5 questions are on us! Inquiry/Problem Solving a) Use the binomial theorem to expand (x y z) 2 by first rewriting it as x ( y z) 2 b) Repeat part a) with (x y z) 3 c) Using parts a) and b), predict the expansion of (x y z) 4Verify your prediction by using the binomial theorem to expand (x y z) 4 d) Write a formula for (x y z) n e) Use your formula to expand and simplify (x y z
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an investor purchases a 181 day UK T bill at a discount of 3 % what is the annualized return 365 days as a percentage of principal input your answer c orre t to three decimal places 2) 24,,12,=Binomial Expansion Calculator is a handy tool that calculates the Binomial Expansion of (xyz)^10 & displays the result ie, x^10 10x^9y 10x^9z 45x^8y^2 90x^8yz 45x^8z^2 1x^7y^3 360x^7y^2z 360x^7yz^2 1x^7z^3 210x^6y^4 840x^6y^3z 1260x^6y^2z^2 840x^6yz^3 210x^6z^4 252x^5y^5 1260x^5y^4z 25x^5y^3z^2 25x^5y^2z^3 1260x^5yz^4Let's have a example x ≥ 0, y ≥ 0, z ≥ 0, x y z = 1, find max of x 2 y y 2 z z 2 x you may think x = y = z = 3 1 is the point of max, but the real one is x = 3 2 , y = 3 1 , z = 0 or
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=x^55x^4z10x^3z^210x^2z^35xz^4z^5 The binomial theorem states that (xy)^nsum_(r=1)^n ""^nC_rx^(nr)y^r therefore (xz)^5=sum_(r=1)^5""^5C_rx^(5r)z^r =""^5C_0x^5""^5C_1x^(51)z^1""^5C_2x^(52)z^2""^5C_3x^(53)z^3""^5C_4x^(54)z^4""^5C_5x^(55)z^5 =x^55x^4z10x^3z^210x^2z^35xz^4z^5To disprove a proposal you need just one case where it does not work Set x = y = x = 1 Left hand side = 3^5 = 243 Right hand side = 3 So the question is answered To find an expression for (x y z)^5 you need Pascal's triangle which evaluates (a b)^n Let b = y z then we can use PascalClick here👆to get an answer to your question ️ Find the coefficient of x^2yz in the expansion of (x y z)^4 Join / Login > 11th > Maths > Binomial Theorem > Special Cases of Binomial Theorem > Find the coefficient of x^2 maths Find the coefficient of x 2 y z in the expansion of (x y z) 4
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See the answer find the coefficient of x^2y^3z^3 in the expansion of (xyz)^8 (121) Show transcribed image text Expert Answer Previous question Next questionCompute answers using Wolfram's breakthrough technology & knowledgebase, relied on by millions of students & professionals For math, science, nutrition, history(xyz)^3 put xy = a (az)^3= a^3 z^3 3az ( az) = (xy)^3 z^3 3 a^2 z 3a z^2 = x^3y^3 z^3 3 x^2 y 3 x y^2 3(xy)^2 z 3(xy) z^2 =x^3 y^3 z^3 3 x
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3 Answers3 For the nontrivial interpretation, you're looking for nonnegative solutions of a b c = n (each of these corresponds to a term x a y b z c ) Code each of these solutions as 1 a 0 1 b 0 1 c, for example ( 2, 3, 5) would be coded as Now it should be easy to see why the answer is ( n 2 n)Therefore, F = m3 m4 m5 m6 m7, which is the same as above when we used term expansion x y z Minterms Notation 0 0 0 x' y' z' m0 0 0 1 x' y' z m1 0 1 0 x' y z' m2 0 1 1 x' y z m3 1 0 0 x y' z' m4 1 0 1 x y' z m5 1 1 0 x y z' m6 1 1 1 x y z m7 Table 39 F = x' y z x y' z x y z' x y zAnswer to A Solve 1 4^x = 16^{2x} \\2 \log_2 8 = x \\3 \log x log (x 3) = 1 B Expand to \log of x, y, and z \log_3
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Expand\3(x6) expand\2x(xa) expand\(2x4)(x5) expand\(2x5)(3x6) expand\(4x^23)(3x1) expand\(x^23y)^3;Expand (xy)^3 (x y)3 ( x y) 3 Use the Binomial Theorem x3 3x2y3xy2 y3 x 3 3 x 2 y 3 x y 2 y 3Click here👆to get an answer to your question ️ Write in expanded form (3x 2y z)^2
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