👉 Learn all about sequences In this playlist, we will explore how to write the rule for a sequence, determine the nth term, determine the first 5 terms or3(x2) = 3x6 Example Expand x(x− y) The x outside must multiply both terms inside the brackets x(x− y) = x2 −xy Example Expand −3a2(3− b) Both terms inside the brackets must be multiplied by −3a2 −3a 2(3−b) = −9a 23a b Example Expand (x5)x Here, the brackets appear first, but the prin ciple is the same Both terms inside must be multiplied by the x outside (x5)xThe formula is (xy)³=x³y³3xy(xy) Proof for this formula step by step =(xy)³ =(xy)(xy)(xy) ={(xy)(xy)}(xy) =(x²xyxyy²)(xy) =(xy)(x²y²2xy
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Quotient of x^38x^217x6 with x3;The following are algebraix expansion formulae of selected polynomials Square of summation (x y) 2 = x 2 2xy y 2 Square of difference (x y) 2 = x 2 2xy y 2 Difference of squares x 2 y 2 = (x y) (x y) Cube of summation (x y) 3 = x 3 3x 2 y 3xy 2 y 3 Summation of two cubes x 3 y 3 = (x y) (x 2 xy y 2) CubeA) Expand (xy)^{3} and (xy)^{3} How are the expansions different?
Answer (1 of 15) Mentally examine the expansion of (xyz)^3 and realize that each term of the expansion must be of degree three and that because xyz is cyclic all possible such terms must appear Those types of terms can be represented by x^3, x^2y and xyz If x^3 appears, so must y^3 and z^3 (xy) 3 expanded has 4 terms, 1 more than the exponent, x 3 x 2 y xy 2 and y 3 x is decreasing from 3 to 0 from left to right, as y increases from 0 to 3 Any number or variable to the 0 power is 1 Then you need the coefficients for each of the 4 terms You can read that off Pascal's triangle 1 11 121 1331 1, 3, 3 and 1 are the coefficients that go with each of the 4 terms to get Welcome to Sarthaks eConnect A unique platform where students can interact with teachers/experts/students to get solutions to their queries Students (upto class 102) preparing for All Government Exams, CBSE Board Exam, ICSE Board Exam, State Board Exam, JEE (MainsAdvance) and NEET can ask questions from any subject and get quick answers by
The 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 expansionThis calculator can be used to expand and simplify any polynomial expression Site map; Expand (xy)^3 We know that (xy) 3 can be written as (xy)(xy)(xy) We know that (xy)(xy) can be multiplied and written as x 2xy yx y 2 (xy) = x 22xy y 2 (xy) = x 32x 2 y xy 2yx 2 2xy 2y 3 = x 33x 2 y 3xy 2y 3 Answer (xy) 3 =x 33x 2 y 3xy 2y 3 Was this answer helpful?
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Expanding brackets To expand a bracket means to multiply each term in the bracket by the expression outside the bracket For example, in the expression \ (3 (mMath Calculators, Lessons and Formulas It is time to solve your math problem mathportalorg Math Tests; 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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Expand the formula of (xy)^3 Get the answers you need, now!Algebra Calculator is a calculator that gives stepbystep help on algebra problems See More Examples » x3=5 1/3 1/4 y=x^21 Disclaimer This calculator is not perfect Please use at your own risk, and please alert us if something isn't working Thank youThe second term of the sum is equal to a$3x^{1/2}y O(x/y)^3$ I think Taylor expansion would do it The thing is, I don't really know around what point I should do it Could anyone help here?Answer and Explanation 1 Become a Studycom member to unlock this answer!
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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 3Expand $(3x^2y)^5$ Ask Question Asked 4 years, 9 months ago Active 4 years, 9 months ago Viewed 154 times 2 1 $\begingroup$ Using binomial theorem we have $\sum_{k=0}^{n} x\displaystyle{8}{x}^{{3}}{12}{x}^{{2}}{y}{6}{x}{y}^{{2}}{y}^{{3}} Explanation In general, for \displaystyle{\left({a}{b}\right)}^{{k}} , the expansion is
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If we examine some simple binomial expansions, we can find patterns that will lead us to a shortcut for finding more complicated binomial expansions \\begin{align*} {(xy)}^2 &= x^22xyy^2 \\4pt {(xy)}^3 &= x^33x^2y3xy^2y^3 \\4pt {(xy)}^4 &= x^44x^3y6x^2y^24xy^3In this problem were given X multiply by three X plus Y, and we multiply the X outside of the brackets with every term that is inside the brackets Now X multiplied by three X We get three X squared plus X, multiplied by Y, we get X Y And this expression cannot be further simplified Since here we have uh, x squared term and here with X Y termsHow to expand two brackets algebra How to simplify (x3)(x4)We can use the distributive law for both x and 3 individually and multiply through
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In 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 positiveRemainder of x^32x^25x7 divided by x3;Expand Using the Binomial Theorem xyz3 x y z3 x y z 3 Use the binomial expansion theorem to find each term Middle School Math Solutions Equation Calculator This is about expansion So its x2 2xy y22 Expand3x6 expand2xxa expand2x4x5 expand2x53×6 expand4x233×1 expandx23y3 Type in any equation to get the solution steps and graph Precalculus The Binomial
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This has both positive and negative terms, so it can be compared with the expansion of (x − y) 3 The terms of polynomials are rearranged Then terms that are perfect cubes are identified Comparing the polynomial with the identity we have, x = 2 a & y = 3 b Using the values of x & y, other terms of the polynomials are written as shown Since x 3 − 3 x 2 y 3 x y 2 − y 3 = (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!Suppose we want to expand (2xy)3 We pick the coefficients in the expansion from the relevant row of Pascal's triangle (1,3,3,1) As we move through the terms in the expansion from left to right we remember to decrease the power of 2x and increase the power of y So, (2xy)3 = 1(2x)3 3(2x)2y 3(2x)1y2 1y3 = 8x3 12x 2y 6xy y3 Example Suppose we want to expand (1p)4
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The expansion of (ax)2 is (ax)2 = a2 2axx2 Hence, (ax)3 = (ax)(ax)2 = (ax)(a2 2axx2) = a3 (12)a 2x(21)ax x 3= a3 3a2x3ax2 x urther,F (ax)4 = (ax)(ax)4 = (ax)(a3 3a2x3ax2 x3) = a4 (13)a3x(33)a2x2 (31)ax3 x4 = a4 4a3x6a2x2 4ax3 x4 In general we see that the coe cients of (a x)n come from the nth row of Pascal's riangleT , inWe know the algebraic expansion of (x y) 3 Rearranging the terms in the expansion, we will get our identity for x 3 y 3 Thus, we have verified our identity mathematically Again, if we replace x with − y in the expression, we have This identity can also be expressed as, This is the required standard algebraic identity In the expression, if we replace y with (− y), we will get the4 (9) (13) (2) Choose An Option That Best Describes Your Problem Answer not
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X^3 y^3 z^3 3x^2y 3xy^2 3x^2z 3z^2x 3y^2z 3z^2y 6xyz Lennox Obuong Algebra Student Email obuong3@aolcomFind the coefficient of x^7 for (x3)^11 Use the binomial theorem to expand (2y3x)^5 Prove that (n over r)= (n over nr) for all integers where n is greater than or equal to r and r is greater than or equal to zero Prove that (n over n2) ( n1 over Texas history Which of the following statements best describes the Galveston hurricane, A Advance warning if the storm led many 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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Expand(1 x y) (2 x)^3 Out16= 8 4 x 6 x^2 5 x^3 x^4 8 y 12 x y 6 x^2 y x^3 y ExpandAllSqrt(1 x)^2 Out17= Sqrt1 2 x x^2 ExpandSinx y, Trig > True Out18= Cosy Sinx Cosx Siny We expand the power expression \( (1x)^{10} \) into a regular polynomial using the following command Expand(1 x)^10 Out19= 11 10 x 45 x^2 1 x^3Expand Master and Build Polynomial Equations Calculator Expand Expresions Write Equation with Roots < Enter Expression < Enter Roots Expand (2x 5) 3 Since (2x 5) 3 is a binomial expansion, we can use the binomial theorem to expand this expression The formula for this is a (x y) n = aΣ k = 0 to n C (n,k) x nk y k where C (nThe first term of the sum is equal to X The second term of the sum is equal to Y The second factor of the product is equal to a sum consisting of 2 terms The first term of the sum is equal to X The second term of the sum is equal to negative Y open bracket X plus Y close bracket multiplied by open parenthesis X plus negative Y close
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Create your account View this answer We can expand x3−y3 x 3 − y 3 using the known identity (x−y)3Removing brackets is to multiply the term outside the brackets by each term inside also known as the distributive law Use FOIL to remove a pair of brackets then simplify by collecting like termsAll Math Calculators Polynomial calculators Expand and Simplify Polynomials;
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The expansion is given by the following formula $$$ \left(a b\right)^{n} = \sum_{k=0}^{n} {\binom{n}{k}} a^{n k} b^{k} $$$, where $$$ {\binom{n}{k}} = \frac{nBinomial Expansions Binomial Expansions Notice that (x y) 0 = 1 (x y) 2 = x 2 2xy y 2 (x y) 3 = x 3 3x 3 y 3xy 2 y 3 (x y) 4 = x 4 4x 3 y 6x 2 y 2 4xy 3 y 4 Notice that the powers are descending in x and ascending in yAlthough FOILing is one way to solve these problems, there is a much easier way243x 5 810x 4 y 1080x 3 y 2 7x 2 y 3 240xy 4 32y 5 Finding the k th term Find the 9th term in the expansion of (x2y) 13 Since we start counting with 0, the 9th term is actually going to be when k=8 That is, the power on the x will 138=5 and the power on the 2y will be 8 The coefficient is either C(13,8) or C(13,5
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My first and naive impression is that the result is 0 but according to Salinas, Introduction to Statistical Physics that's $3x^{1/2}y O(x/y)^3$ I think Taylor expansion would do it The thingNow, we have the coefficients of the first five terms By the binomial formula, when the number of terms is even, then coefficients of each two terms that are at The Binomial Theorem isLearn about expand using our free math solver with stepbystep solutions Microsoft Math Solver Solve Practice Download Solve Practice Topics PreAlgebra Mean Mode Greatest Common Factor Least Common Multiple Order of Operations Fractions Mixed Fractions Prime Factorization Exponents Radicals Algebra Combine Like Terms Solve for a Variable Factor ExpandExpand polynomial (x3)(x^35x2) GCD of x^42x^39x^246x16 with x^48x^325x^246x16;
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B) Show that (xy)^{3}(xy)^{3}=2 x\\left(x^{2}3 y^{2}\\right) c) What is the result forExpand (x2)^3 (x 2)3 ( x 2) 3 Use the Binomial Theorem x3 3x2 ⋅23x⋅ 22 23 x 3 3 x 2 ⋅ 2 3 x ⋅ 2 2 2 3 Simplify each term Tap for more steps Multiply 2 2 by 3 3 x 3 6 x 2 3 x ⋅ 2 2 2 3 x 3 6 x 2 3 x ⋅ 2 2 2 3 Raise 2 2 to the power of 2 218 Following Scripts Print Syms Xy F X Y 3 Expand F B Factor Syms X Y F X Y 3 Expand F B D QMATLAB18 What will the following scripts print?
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If we wanted to expand \({(xy)}^{52}\), we might multiply \((xy)\) by itself fiftytwo times This could take hours!View more examples » Access instant learning tools Get immediate feedback and guidance with stepbystep solutions and Wolfram Problem Generator Hi Heureka, I am wondering if it can still be done easily if it is made more complicated ?
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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 CancelExpand 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 Special expansions online The function expandThe coefficients of each expansion are the entries in Row n of Pascal's Triangle Thus, the coefficient of each term r of the expansion of (x y) n is given by C(n, r 1) The exponents of x descend, starting with n, and the exponents of y ascend, starting with 0, so the r th term of the expansion of (x y) 2
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(x y) 5 = x 5 5x 4 y 10x 3 y 2 10x 2 y 3 5xy 4 y 5 Look familiar?Thank you taylorexpansion Share Cite Follow edited Mar 9 '16 at 024 Michael Hardy 257k 28 28 gold badges 258 258 silver badges 549 549 bronze badges asked Mar 9 '16 at 000 Patrick Patrick 219 2 2 silver badges 9(c) Factorise completely 8)' (b) Expand 5p(p — 3) 12 x 6 (a) Expand 3(4x y) (2) (6 marks) Factorise comt)letelv (2) 21?4 Expand Factorise
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