Stack Exchange network consists of 176 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 ExchangeTo ask Unlimited Maths doubts download Doubtnut from https//googl/9WZjCW In the expansion of `(x y z)^25`2 Convert x2y2z2 x 2 y 2 z 2 to r2 r 2 3 Use binomial expansion to simplify from PHYS ELECTRICIT at University of Santo Tomas
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On expanding the expression (x+y-z)2 becomes
On expanding the expression (x+y-z)2 becomes-Expand ( X Y Z )2 Mathematics Sum Expand ( x y z ) 2So we've got 3y squared plus 6x to the third we're raising this whole thing to the fifth power and we could clearly use a binomial theorem or Pascal's triangle in order to find the expansion of that but what I want to do really is a as an exercise is to try to hone in on just one of the terms and in particular I want to hone in on the term that has some coefficient times X to the sixth Y to
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Learn about expand using our free math solver with stepbystep solutionsFree PreAlgebra, Algebra, Trigonometry, Calculus, Geometry, Statistics and Chemistry calculators stepbystepWhen we expand latex{\left(xy\right)}^{n}/latex by multiplying, the result is called a binomial expansion, and it includes binomial coefficientsIf we wanted to expand latex{\left(xy\right)}^{52}/latex, we might multiply latex\left(xy\right)/latex by itself fifty
WolframAlpha brings expertlevel knowledge and capabilities to the broadest possible range of people—spanning all professions and education levelsLearn how to solve special products problems step by step online Expand the expression (x2y3z)^2 Expand the trinomial using the formula \left(abc\right)^2 = a^2 b^2 c^2 2ab 2ac 2bc Multiply 2 times 2 Multiply 2 times 3 Multiply 2 times 2The second term above, with just a "5" inside, is as "expanded" as it can get, because there's only just the one thing inside the logAnd, because 5 is not a power of 2, there's no simplification I can doSo that part of the expansion is done;
Dec 05, 17 · Visit our website https//wwwMinuteMathTutorcomConsider supporting us on Patreonhttps//wwwpatreoncom/MinuteMathProperties of LogarithmsExpand log(x•Therefore f(x,y) = y xy 10Expand xy2x3y2 in powers of (x1) & (y2) using tailors theorem upto first degree terms Find the extreme values of the function u = x2y2z2 subject to axbycz = P 6 Expand exlogy in a series of positive powers of x and (y1) up to terms of thirdMay 21, 19 · Expand (i) (3x – 4y 5z)2 (ii) (2a – 5b – 4c)2 (iii) (5x 3y)3 (iv) (6a – 7b)3
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The question that I have to solve is an answer on the question "How many terms are in the expansion?" Depending on how you define "term" you can become two different formulas to calculate the terms in the expansion of $(xyz)^n$ Working with binomial coefficients I found that the general relation is $\binom{n2}{n}$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 log log y y æ ö æ ö = ç ÷ ç ÷ ç ÷ ç ÷ Ł ł Ł ł Rewrite the radical using rational exponents (fractions) 1 3 2 8 8 = logxlogy Use property 4 to rewrite the division as subtractionExpand the following product (3 x 1) (2 x 4) `(3x1)(2x4)` returns `3*x*2*x3*x*42*x4` Expand this algebraic expression `(x2)^3` returns `2^33*x*2^23*2*x^2x^3` Note that the result is not returned as the simplest expression in order to be able to follow the steps of calculations To simplify the results, simply use the reduce function
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Remainder of x^32x^25x7 divided by x3;Apr 10, 18 · 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 terms in the other brackets, but never multiply two or more terms in the same bracket Answer linkfirst take it to be real, δz = δx Then f0(z) = lim δx→0 f(z δx)−f(z) δx = lim δx→0 u(xδx,y)iv(xδx,y)−u(x,y)−iv(x,y) δx = lim δx
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Mar 16, 17 · Ex 25, 4 Expand each of the following, using suitable identities (x 2y 4z)2 (x 2y 4z)2 Using (a b c)2 = a2 b2 c2 2ab 2bc 2ac Where a = x , bExample 2 if x = 10 and y is 4 (10 4) 2 = 10 2 2·10·4 4 2 = 100 80 16 = 36 The opposite is also true 25 a 4a 2 = 5 2 2·2·5 (2a) 2 = (5 2a) 2 Consequences of the above formulasA "true" value 1 2A Axioms XY = Y X X Y = Y X X(Y Z) = (XY)Z X (Y Z) = (X Y)Z X(X Y) = X X (XY) = X X (Y Z) = (X Y)(X Z) X(Y Z) = (XY)(XZ) XX = 1 X X = 0 We will use the first nontrivial Boolean Algebra A = {0,1} This adds the law of excluded middle if X 6=0 then X = 1 and if X 6=1 then X = 0
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Algebra Expand (xyz)^2 (x − y − z)2 ( x y z) 2 Rewrite (x−y −z)2 ( x y z) 2 as (x−y−z)(x−y−z) ( x y z) ( x y z) (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 byIn 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}yClick here👆to get an answer to your question ️ The coefficients of x^2y^2,yzt^2,xyzt and in the expansion of (x y z t)^4 are in the ratio
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Expand (x 2 y 3 z) 2 Easy View solution State whether the statement is True or False The square ofSeparate f and z into real and imaginary parts f(z) = u(x,y)iv(x,y) where z = x iy and u, v are real functions Suppose that f is differentiable at z We can take δz in any direction;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 z
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Compute answers using Wolfram's breakthrough technology & knowledgebase, relied on by millions of students & professionals For math, science, nutrition, historyExpand polynomial (x3)(x^35x2) GCD of x^42x^39x^246x16 with x^48x^325x^246x16;Given x^2y^2z^2=xyyzzx (1)multiplying by (xyz) on both sidesx^2y^2z^2 (xyz)=(xyyzzx ) (xyz)expand the above equationsx^3y^3z^3xy^2x^2 yyz^2y^2 zxz^2x^2 z=x^2 yxyzzx^2xy^2 y^2 zxyzxyz
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(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 FinalView more examples » Access instant learning tools Get immediate feedback and guidance with stepbystep solutions and WolframProof Let x y = k then, (x y z)2 = (k z)2 = k2 2kz z2 (Using identity I) = (x y)2 2( x y)z z2 = x2 2xy y2 2 xz 2yz z2 = x2 y2 z2 2xy 2yz 2zx i hope it is a good answer pls mark as brainliest
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Apr 22, 10 · Try the Multinomial theorem The coefficient of x^a*y^b*z^c in the expansion of (x y z)^n is n!/(a!Algebra Expand (xyz)^2 (x − y z)2 ( x y z) 2 Rewrite (x−y z)2 ( x y z) 2 as (x−yz)(x−yz) ( x y z) ( x y z) (x−y z)(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 expressionFrom above answers we have (xyz)³=x³y³z³3(x²yx²zy²xy²zz²xz²y2xyz) Now, factorizing the expression "x²yx²zy²xy²zz²xz²y2xyz" makes this identify beautiful So, x²yx²zy²xy²zz²xz²y2xyz= x²yy²xy²zxyzx²zz²xz²yxyz (Just spill
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For example, suppose that we want to expand the trinomial $(x y z)^3$ We will have there be $\binom{3 3 1}{3} = \binom{5}{3} = 10$ nonnegative integer solutions to this equation They are the ordered pairs $(r_1, r_2, r_3)$ given in the table below $(3, 0, 0)$ $(0, 3, 0)$ $(0, 0, 3)$ $(2, 1, 0)$ $(2Free expand & simplify calculator Expand and simplify equations stepbystep This website uses cookies to ensure you get the best experience By using this* c!) Thus, the required coefficient is
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The Binomial Theorem Here is the expansion of (x y)n for n = 0, 1,, 5 (x y)0 = 1 (x y)1 = x y (x y)2 = x2 2xy y2 (x y)3 = x3 3x2y 3xy2 y3 (x y)4 = x4 4x3y 6x2y2 4xy3 y4 (x y)5 = x5 5x4y 10x3y2 10x2y3 5xy4 y5 Look familiar?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) zI'll just be carrying the "log(5)" along for
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Mar , 18 · (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, zSince (3x z) is in parentheses, we can treat it as a single factor and expand (3x z)(2x y) in the same manner as A(2x y) This gives us If we now expand each of these terms, we have Notice that in the final answer each term of one parenthesesComplex arithmetic Sums In order to add two complex numbers, we separately add their real and imaginary parts, (x 1 iy 1) (x 2 iy 2) = (x 1 x 2) i(y 1 y 2) The complex conjugate of x iy is defined to be x iyThe complex conjugate of a complex number z is written z *Notice that
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Feb 10, 08 · leao 1 decade ago well for (xy)^2, the expansion is the square of each term plus twice the sum of the pairwise combinations of the terms which isFor example, a univariate (singlevariable) quadratic function has the form = ,in the single variable xThe graph of a univariate quadratic function is a parabola whose axis of symmetry is parallel to the yaxis, as shown at right If the quadratic function is set equal to zero, then the result is a quadratic equationThe solutions to the univariate equation are called the roots of theThe 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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