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Click here👆to get an answer to your question ️ Expansion of (a b)^3 isO 1, 4, 6, 4, 1 O 1,1 O 1, 2,1 O 1,3,3, 1 2 See answers esbeydeeromero esbeydeeromero The fourth option I got that last time happy244 happy244 Answer D Stepbystep explanation New questions in MathematicsWhat are the coefficients for the binomial expansion of (a b)3?

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(a+b)^3 expanded-(ab)^3=(ab)(a^22abb^2) We will now expand these two brackets, first multiplying the a in the lefthand bracket by everything in the righthand bracket, and then multiplying the b in the lefthand bracket by everything in the righthand bracket Doing so, we get, (ab)(a^22abb^2)=a^32a^2bab^2a^2b2ab^2b^3= 8x 3 36x 2 y 54xy 2 27y 3 8x 3 36x 2 y 54xy 2 27y 3 = 72x 2 y 54y 3 If you would like to contribute notes or other learning material, please submit them using the button below

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Example Expand 3 × (52) Answer It is now expanded We can also complete the calculation 3 × (52) = 3 × 5 3 × 2 = 15 6 = 21 In Algebra In Algebra putting two things next to each other usually means to multiply So 3(ab) means to multiply 3 by (ab) Here is an example of expanding, using variables a,If not, which expansion should I look up to do so?In mathematics, the expanded form of a number is defined as the notation It is the way of writing the numbers to define the individual digit value When the numbers are written using place value, it will create a new algebraic

= 8x 3 36x 2 y 54xy 2 27y 3 8x 3 36x 2 y 54xy 2 27y 3 = 72x 2 y 54y 3 If you would like to contribute notes or other learning material, please submit them using the button belowIn 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 integer dependingTo get `tan(x)sec^3(x)`, use parentheses tan(x)sec^3(x) From the table below, you can notice that sech is not supported, but you can still enter it using the identity `sech(x)=1/cosh(x)` If you get an error, doublecheck your expression, add parentheses and multiplication signs where needed, and consult the table below

To find an expansion for (a b) 8, we complete two more rows of Pascal's triangle Thus the expansion of is (a b) 8 = a 8 8a 7 b 28a 6 b 2 56a 5 b 3 70a 4 b 4 56a 3 b 5 28a 2 b 6 8ab 7 b 8 We can generalize our results as follows The Binomial Theorem Using Pascal's Triangle For any binomial a b and any natural number n,Introduction to a minus b whole cube identity with example problems and proofs to learn how to derive ab whole cube formula in mathematicsTo find an expansion for (a b) 8, we complete two more rows of Pascal's triangle Thus the expansion of is (a b) 8 = a 8 8a 7 b 28a 6 b 2 56a 5 b 3 70a 4 b 4 56a 3 b 5 28a 2 b 6 8ab 7 b 8 We can generalize our results as follows The Binomial Theorem Using Pascal's Triangle For any binomial a b and any natural number n,

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The expansion of (ab)^3 is(ab)^3 (a b)^3 ( a b ) ^ 3 ( a b ) ^ 3 and this will go on for ever Just write the expression on your page and see the miracle(a 3 3a 2 b 3ab 2 b 3)(ab) = a 4 4a 3 b 6a 2 b 2 4ab 3 b 4 The calculations get longer and longer as we go, but there is some kind of pattern developing That pattern is summed up by the Binomial TheoremExpansion The cube of difference between any two terms is expanded as the subtraction of three times the product of both terms and the subtraction of the second term from the first term, from the subtraction of the cube of the second term from the cube of the first term $\implies$ $(ab)^3$ $\,=\,$ $a^3b^33ab(ab)$ Simplification

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You can check the formulas of A plus B plus C Whole cube in three ways We are going to share the (abc)^3 algebra formulas for you as well as how to create (abc)^3 and proof weCompute answers using Wolfram's breakthrough technology & knowledgebase, relied on by millions of students & professionals For math, science, nutrition, historyPrecalculus The Binomial Theorem The Binomial Theorem 1 Answer

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A Plus B Plus C Whole cube Are you looking for A plus B plus C Whole cube?How do you use the binomial formula to expand #(x1)^3#?Prentice Hall Mathematics, Algebra 2 (0th Edition) Edit edition Problem 69E from Chapter 68 What is the expanded form of (a − b)3?A a3 a2b ab2 b3 Get solutions

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Make a Pascal's triangle down to the line that starts with 1 4 Start with thisBut there's three ways to get to a squared b And you could multiply it out, and we did it We did it all the way back over here There's three ways to get a squared b We saw that right over there And there are three ways to get a b squared Three ways to get a b squared And if you sum this up you have the expansion of a plus b to the thirdStep 3 Finally, the expanded form of a number will be displayed in the output field What is Meant by Expanded Form?

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Pascal's triangle can be used to find the coefficient of binomial expansion (a b) 0 1 (a b) 1 1 1 (a b) 2 1 2 1 (a b) 3 1 3 3 1 (a b) 4 1 4 6 4 1 (a b) 5 1 5 10 10 5 1 (a b) 6 1 6 15 15 6 1F (x) = x^3 b^3 x=b is a root of f (x), so we can divide (xb) by any method you choose The quotient will be x^2 bx b^2 which shows that x^3 b^3 = (xb) (x^2 bx b^2) Then, setting x = a, we have the same factorization as above Show more(a b) 3 = a 3 3a 2 b 3ab 2 b 3 or (a b) 3 = a 3 b 3 3ab(a b) Practice Problems Problem 1 Expand (x 1) 3 Solution (x 1) 3 is in the form of (a b) 3 Comparing (a b) 3 and (x 1) 3, we get a = x b = 1 Write the formula / expansion for (a b) 3 (a b) 3 = a 3 3a 2 b 3ab 2 b 3 Substitute x for a and 1

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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 expansion of an expressionExpand using Pascal's Triangle (ab)^6 Pascal's Triangle can be displayed as such The triangle can be used to calculate the coefficients of the expansion of by taking the exponent and adding The coefficients will correspond with line of the triangle For ,(a 3 3a 2 b 3ab 2 b 3)(ab) = a 4 4a 3 b 6a 2 b 2 4ab 3 b 4 The calculations get longer and longer as we go, but there is some kind of pattern developing That pattern is summed up by the Binomial Theorem

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Definition binomial A binomial is an algebraic expression containing 2 terms For example, (x y) is a binomial We sometimes need to expand binomials as follows (a b) 0 = 1(a b) 1 = a b(a b) 2 = a 2 2ab b 2(a b) 3 = a 3 3a 2 b 3ab 2 b 3(a b) 4 = a 4 4a 3 b 6a 2 b 2 4ab 3 b 4(a b) 5 = a 5 5a 4 b 10a 3 b 2 10a 2 b 3 5ab 4 b 5Clearly, doing this byHow to expand (ab)(ab) to equal a^2b^2?The steps to expand two brackets is to multiply each term in the first bracket with each term in the second bracketThe cube of the sum of two terms is expanded as the sum of cubes of both terms and three times the product of both terms and sum of them ⟹ (a b) 3 = a 3 b 3 3 a b (a b)

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(a b) 3 = a 3 3a 2 b 3ab 2 b 3 or (a b) 3 = a 3 b 3 3ab(a b) Solved Problems Problem 1 Expand (x 2) 3 Solution (x 2) 3 is in the form of (a b) 3 Comparing (a b) 3 and (x 2) 3, we get a = x b = 2 Write the formula / expansion for (a b) 3 (a b) 3 = a 3 3a 2 b 3ab 2 b 3 Substitute x for a and 2 for b= (a b)(a b)(a b) = (a b)(a² ab ab b²) = (a b)(a² 2ab b²) = a³ 2a²b ab² a²b 2ab² b³ = a³ 3a²b 3ab² b³Expansion of $(ab)^{1/3}$ with binomial theorem Ask Question Asked 2 years, 11 months ago Active 2 years, 11 months ago Viewed 1k times 1 $\begingroup$ I want to expand $(ab)^{1/3}$ using the binomial theorem 1) Is it possible to do that?

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A B 3 Expansion Source(s) https//shrinkeim/bak2d 0 0 Judith Lv 4 5 years ago For the best answers, search on this site https//shorturlim/avcp8 The key synthesizer workstations such as Roland Fantom X8, Yamaha Motif ES8 and Korg Triton Studio have the hammerweighted key feel of an acoustic piano The sound depends on theSolved Write in expanded form (2a b)^{3} By signing up, you'll get thousands of stepbystep solutions to your homework questions You can alsoPascal's triangle can be used to find the coefficient of binomial expansion (a b) 0 1 (a b) 1 1 1 (a b) 2 1 2 1 (a b) 3 1 3 3 1 (a b) 4 1 4 6 4 1 (a b) 5 1 5 10 10 5 1 (a b) 6 1 6 15 15 6 1

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Expansion of $(ab)^{1/3}$ with binomial theorem Ask Question Asked 2 years, 11 months ago Active 2 years, 11 months ago Viewed 1k times 1 $\begingroup$ I want to expand $(ab)^{1/3}$ using the binomial theorem 1) Is it possible to do that?Question Multiply to find the expanded form of each product 1 (a b)^2 2 (a b)^3 3 (a b)^4 Answer by Edwin McCravy() (Show Source) You can put this solution on YOUR website!^3 a^2b ab^2 b^3 ba^3 a^2b ab^2 b^3 ca^3 3a^2b 3ab^2 b^3 da^3 3a^2b 3ab^2 b^3 How legal titan Tom Girardi seduced the Calif State Bar

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(abc) 3 a 3 b 3 c 3 We can choose three "a"'s for the cube in one way C(3,3)=1, or we can choose an a from the first factor and one from the second and one from the third, being the only way to make a3 The coefficient of the cubes is therefore 1 (It's the same for a, b and c, of course) 3a 2 b3a 2 c Next, we consider the a 2 terms WeCube Formulas (a b) 3 = a 3 b 3 3ab (a b) (a − b) 3 = a 3 b 3 3ab (a b) a 3 − b 3 = (a − b) (a 2 b 2 ab) a 3 b 3 = (a b) (a 2 b 2 − ab) (a b c) 3 = a 3 b 3 c 3 3 (a b) (b c) (c a) a 3 b 3 c 3 − 3abc = (a b c) (a 2 b 2 c 2 − ab − bc − ac) If (a b c) = 0,Pascal triangles gives us the coefficients for an expanded binomial of the form (ab)n,where n is now the row of the triangle shanmso2 shanmso2 The coefficients of the terms come from rows of the triangle If the exponent is n, look at the entries in row n New questions in Mathematics

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Example Expand 3 × (52) Answer It is now expanded We can also complete the calculation 3 × (52) = 3 × 5 3 × 2 = 15 6 = 21 In Algebra In Algebra putting two things next to each other usually means to multiply So 3(ab) means to multiply 3 by (ab) Here is an example of expanding, using variables a,1 3 3 1Free expand & simplify calculator Expand and simplify equations stepbystep

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Compute answers using Wolfram's breakthrough technology & knowledgebase, relied on by millions of students & professionals For math, science, nutrition, history(x 3) 3 We know that (a b) 3 = a 3 3a 2 b 3ab 2 b 3 In the given example, a = x and b = 3 ∴ `(x 3)^3 = (x)^3 3 xx x^2 xx 3 3 xx x xx (3)^2 (3)^3` ∴ `(x 3)^3 = x^3 9x^2 27x 27`(ab)^6 ANSWER Pascal's Triangle It is a triangle of numbers, which is given below 1 1 1 1 2 1 1 3 3 1 1 4 6 4 1 1 5 10 10 5 1 1 6 15 15 6 1 1 7 21 35 35 21 7 1 1 8 28 56 70 56 28 8 1 1 9 36 84 126 126 84 36 9 1 Each number in the triangle is the sum of two above For example, the 6 on line 5 is the sum of the pair of 3's above So the

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Expanded form calculator shows expanded forms of a number including expanded notation form, expanded factor form, expanded exponential form and word form Expanded form or expanded notation is a way of writing numbers to see the math value of individual digits When numbers are separated into individual place values and decimal places they can

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