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 random(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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(x+y+z)^3 expand-Expand each of the following, using suitable identities (− 2 x 3 y 2 z) 2 Easy Answer (− 2 x 3 y 2 z) 2 For example, (xyz) 3 = ((xy) z) 3 = (xy) 3 3(xy) 2 z 3(xy)z 2 z 3 Then, expand the (xy) terms using the Binomial Theorem (x 3 3x 2 y 3xy 2 y 3 ) 3(x 2 2xy y 2 )z 3xz 2 3yz 2 z 3
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Use the power rule for logarithms to expand the expression Write your answer in reduced form ln⎛⎝√ (y2 −9)(y 4)7 y3 ⎞⎠ ln ( ( y 2 9) ( y 4) 7 y 3) Get help Box 1 Enter your answer as an expression Example 3x^21, x/5, (ab)/c Be sure(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 y * y = y^2 y * z = yz z * x = xz z * y = yz z * z = z^2 We now have x^2 xy xz xy y^2 yz xz yz z^2 Combine like terms xy xy =2xy xz xz = 2xz yz yz = 2yz Therefore x^2 y^2 z^2 2xy 2xz 2yzF = x y z = x (y z) AND (multiply) has a higher precedence than OR (add) = (x y) (x z) use distributive law to change to product of OR terms = (x y z z') (x y y' z) expand 1st term by ORing it with z z', and 2nd term with y y' = (x y z) (x y z') (x y z) (x y' z) = M0 • M1 • M2 = Π(0, 1, 2) product of 0
#(xy)^3=(xy)(xy)(xy)# Expand the first two brackets #(xy)(xy)=x^2xyxyy^2# #rArr x^2y^22xy# Multiply the result by the last two brackets #(x^2y^22xy)(xy)=x^3x^2yxy^2y^32x^2y2xy^2# #rArr x^3y^33x^2y3xy^2#A Taylor Series is an expansion of some function into an infinite sum of terms, where each term has a larger exponent like x, x 2, x 3, etc Example The Taylor Series for e x e x = 1 x x 2 2!Visit our website https//wwwMinuteMathTutorcomConsider supporting us on Patreonhttps//wwwpatreoncom/MinuteMathProperties of LogarithmsExpand log(x•
=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^5Expand (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 ️ 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 is
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In elementary algebra, the binomial theorem describes the algebraic expansion of powers of a binomial According to the theorem, it is possible to expand the polynomial n into a sum involving terms of the form axbyc, where the exponents b and c are nonnegative integers with b c = n, and the coefficient a of each term is a specific positive integer depending on n and b For example, 4 = x 4 4 x 3 y 6 x 2 y 2 4 x y 3 y 4 {\displaystyle ^{4}=x^{4}4x^{3}y6x^{2}y^{2}4xy^{3}yThis calculator can be used to expand and simplify any polynomial expression (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
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Expand ( X Y Z )2 CISCE ICSE Class 9 Question Papers 10 Textbook Solutions Important Solutions 5 Question Bank Solutions Concept Notes & Videos 242 Syllabus Advertisement Remove all ads Expand ( X Y Z )2 MathematicsTaylor series and Maclaurin series LinksTaylor reminder theorem log(11)≈01 ((01)^2/2)((01)^3/3) Find minimum error and exact value https//youtubeCompute answers using Wolfram's breakthrough technology & knowledgebase, relied on by millions of students & professionals For math, science, nutrition, history
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Expand (xy)(zwt) I got xzxwxtyzywyt I feel like I'm wrong though Any help is greatly appreciated 0 comments share save hide report 100% Upvoted Log in or sign up to leave a comment Log In Sign Up Sort by best no comments yet Be the first to share what you think!3 Answers3 Note that just as you can use Pascal's Triangle for binomials, you can use Pascal's Pyramid for trinomials Otherwise, you can use the Multinomial Theorem as Jp McCarthy suggested Hint ( x y z) k ≡ x ( y z) k Now use the binomial formula forClick 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)
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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 = Expand (i) (3x – 4y 5z)2 (ii) (2a – 5b – 4c)2 (iii) (5x 3y)3 (iv) (6a – 7b)3Algebra Examples Rewrite (x−y z)2 ( x y z) 2 as (x−yz)(x−yz) ( x y z) ( x y z) Expand (x−yz)(x−yz) ( x y z) ( x y z) by multiplying each term in the first expression by each term in the second expression
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To 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`As you can see for ( a b) n contains just n 1 terms Note that we have to keep the sum of powers in each of the combinations of x, y, z to n, so it will be reduced Now replace a and b by x and ( y z) respectively So total number of terms should be 1 2 3Expandcalculator 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
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Algebra Expand 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 ∑To 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 PascalSimilar Problems from Web Search (xyz) (xzxyyz)xyz Final result x2y x2z xy2 2xyz xz2 y2z yz2 Step by step solution Step 1 Equation at the end of step 1 (x y z) • (xy xz yz) xyz Step 2 Final
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Expand\3(x6) expand\2x(xa) expand\(2x4)(x5) expand\(2x5)(3x6) expand\(4x^23)(3x1) expand\(x^23y)^3;Suyeon Khim contributed The multinomial theorem describes how to expand the power of a sum of more than two terms It is a generalization of the binomial theorem to polynomials with any number of terms It expresses a power ( x 1 x 2 ⋯ x k) n (x_1 x_2 \cdots x_k)^n (x1The calculator can also make logarithmic expansions of formula of the form ln ( a b) by giving the results in exact form thus to expand ln ( x 3), enter expand_log ( ln ( x 3)) , after calculation, the result is returned The calculator makes it possible to obtain the logarithmic expansion
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Use the following identity which also gives you the exact deviation in positive terms from $27 x y z$ (from which you can derive tighter bounds of the LHS) $$ (xyz)^3 = 27 x y z 3 (zy)^2 x 3 (xz)^2 y 3 (yx)^2 z \\ \frac12 (xyz)((xy)^2 (yz)^2 (zx)^2) $$ All terms on the RHS are positive, so you can take lower bounds of theThe 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 ⋅ xSimplify (xy)(xy) Expand using the FOIL Method Tap for more steps Apply the distributive property Apply the distributive property Apply the distributive property Simplify terms Tap for more steps Combine the opposite terms in Tap for more steps
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WolframAlpha brings expertlevel knowledge and capabilities to the broadest possible range of people—spanning all professions and education levelsLog 2 (8) log 2 ( x4) – log 2 (5) = 3 4 log 2 ( x) – log 2 (5) Each log now finally contains only one thing, and the first log term has been simplified to a numerical value, so this expression is fully expanded Then my final answer is 3 4log 2 ( x) – log 2 (5) Content Continues BelowStart your free trial In partnership with You are being redirected to Course Hero I want to submit the same problem to
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5!) Thus, (xyz) 10 = ∑(10!) / (P1Consider the expansion of (x y z) 10 In the expansion, each term has different powers of x, y, and z and the sum of these powers is always 10 One of the terms is λx 2 y 3 z 5 Now, the coefficient of this term is equal to the number of ways 2x′s, 3y′s, and 5z′s are arranged, ie, 10!Rewrite (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 x
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Solve x y z = x 3 y 3 z 3 = 8 in Z First I tried to transform this equation, substituting x = 8 − y − z So I end up with x 3 y 3 z 3 = 8 ( 8 − y − z) 3 y 3 z 3 = 8 Using Wolfram Alpha I expanded this equation and tried to factorize it so finally I got ( z − 8) ( y 2 y ( z − 8) − 8 z) = 168If we replace y with (− y) the expression changes to (x − y) 3 So to find the expansion of ( x − y ) 3 , we can replace y with ( − y ) in ( x y ) 3 = x 2 3 x 2 y 3 x y 2 y 3 This is the required expansion for ( x − y ) 3Our 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!
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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;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 solve for x with explanation dont spam or i will report tex\frac{4}{x} = 0/tex by what rational be 25/2is divided to get 19/3 a Boat is Road downstream at 155 km H and higher and upstream at 85 km the speed of the stream is
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