√ (a+b)^3 formula expansion 130628-How to expand a^3-b^3

=SUM(*$E$29,C3*$E$30,D3*$E$31) by the way you can have the short cut by clicking the E29 in the formula bar and press F4 on your keyboard it will result like above formula The meaning of the $ dollar sign in the cell address is to make it fix and constant(abcde) 3 a 3 b 3 c 3 d 3 e 3 As usual, the cubics have a coefficient 1 There are 5 different letters, so we have 5 cubics The sum of the coefficients is 1·5=5 3a²b3a²c3a²d3a²e 3b²a3b²c3b²d3b²e 3c²a3c²b3c²d3a²e 3d²a3d²b3d²c3d²e 3e²a3e²b3e²c3e²d= 3*2*1 = 6, 2!

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How to expand a^3-b^3

How to expand a^3-b^3-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}y^{4}} TheLet the literals a and b represent two terms in algebraic form The subtraction of b from a is written as a − b It is basically an algebraic expression and also a binomial The square of this expression is written as ( a − b) 2 in mathematical form and it is expanded as a 2 − 2 a b b 2 mathematically In mathematics, this algebraic identity is used as a formula and it is called in the following three ways

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(a b) 3 = a 3 b 3 3ab(a b) (a – b) 3 = a 3 – 3a 2 b 3ab 2 – b 3 = a 3 – b 3 – 3ab(a – b) a 3 – b 3 = (a – b)(a 2 ab b 2 )A^3 3a^2b 3ab^2 b^3 Use the Binomial expansion (note the exponents sum to the power in each term) (xy)^3 = _3C_0x^3y^0 _3C_1x^2y^1 _3C_2x^1y^2 _3C_3x^0y^3 Remember 3!A1/3 a1/3 a1/3 = a (24) (a1/3)3 = a (25) (a2)1/3 = (a1/3)2 = a2∕3 (26) (a1/3)1/4 = a1/3 1/4 = (a1/4)1/3 (27) (a b)1/3 = a1/3 b1/3 (28) (a / b)1/3 = a1/3 / b1/3 (29) (1 / a)1/3 = 1 / a1/3 = a1/3 (30) Sponsored Links Mathematics Mathematical rules and laws numbers, areas, volumes, exponents, trigonometric functions and more

That is, for each term in the expansion, the exponents of the x i must add up to n Also, as with the binomial theorem, quantities of the form x 0 that appear are taken to equal 1 (even when x equals zero) In the case m = 2, this statement reduces to that of the binomial theorem Example The third power of the trinomial a b c is given by= 1 and 0!(a b) 2 = (a b)(a b) = a 2 2ab b 2 (a − b) 2 = (a − b)(a − b) = a 2 − 2ab b 2 Example 3 Expand the given expression, clicking on the equal signs to see the next step (

A 3 – b 3 = (a – b) (a 2 ab b 2) a 3 b 3 = (a b) (a 2 – ab b 2) (a b) 3 = a 3 3a 2 b 3ab 2 b 3 (a – b) 3 = a 3 – 3a 2 b 3ab 2 – b 3 (a b – c) 2 = a 2 b 2 c 2 2ab – 2bc – 2ca (a – b c) 2 = a 2 b 2 c 2 – 2ab – 2bc 2ca (a – b – c) 2 = a 2 b 2 c 2 – 2ab 2bc – 2ca (a b c) 2 = a 2 b 2 c 2 2ab 2bc 2caPipes Heat Expansion and Cooling Contraction Expansion or contraction when heating or cooling cast iron, carbon and carbon molybdenum steel, wrought iron, copper, brass and aluminum pipes Pipes and Tubes Temperature Expansion Pipes expands when heated and contracts when cooled and the expansion can be expressed with the expansion formulaEuler's formula then comes about by extending the power series for the exponential function to the case of x= i to get exp(i ) = 1 i 2 2!

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Binomial Theorem The Expansion of (a b)n If n is any positive integer, then ( a b) n = a n n C 1 a n − 1 b n C 2 a n − 2 b 2 ⋯ n C m a n − m b m ⋯ b n Where n C m = combination of n objects taken m at a time Some Example of Binomial Expansion ( a b) 2 = a 2 2 a b b 2 ( a b) 3 = a 3 3 a 2 b 3 a b 2 b 3Solution We have (a b) n, where a = 2/x, b = 3√ x, and n = 4 Then using the binomial theorem, we have Then using the binomial theorem, we have Finally (2/x 3√ x ) 4 = 16/x 4 96/x 5/2 216/x 216x 1/2 81x 2A³ b³ = (a b)(a² – ab b²)

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Binomial theorem, statement that for any positive integer n, the nth power of the sum of two numbers a and b may be expressed as the sum of n 1 terms of the form in the sequence of terms, the index r takes on the successive values 0, 1, 2,, n The coefficients, called the binomial coefficients, are defined by the formula(a b) 3 = a 3 b 3 3ab(a b) (a – b) 3 = a 3 – 3a 2 b 3ab 2 – b 3 = a 3 – b 3 – 3ab(a – b) a 3 – b 3 = (a – b)(a 2 ab b 2 )Expansions Which Have LogarithmBased Equivalents Summantion Expansion Equivalent Value Comments x n

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In algebra, a quadratic equation (from the Latin quadratus for "square") is any equation that can be rearranged in standard form as = where x represents an unknown, and a, b, and c represent known numbers, where a ≠ 0If a = 0, then the equation is linear, not quadratic, as there is no term The numbers a, b, and c are the coefficients of the equation and may be distinguished by callingOne way to Do this, is to first learn what is (A B) ^3 by just multiplying A B with itself 3 times and you will have (A B)^3 = A^3 3A^2B 3AB^2 B^3 Now replace A by a and B by (b c) and Do the Work !In mathematics, a trinomial expansion is the expansion of a power of a sum of three terms into monomials The expansion is given by ( a b c ) n = ∑ i j k = n i , j , k ( n i , j , k ) a i b j c k , {\displaystyle (abc)^ {n}=\sum _ {\stackrel {i,j,k} {ijk=n}} {n \choose i,j,k}\,a^ {i}\,b^ {\;\!j}\;\!c^ {k},}

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(a b) 3 = a 3 3a 2 b 3ab 2 b 3;In mathematics, a trinomial expansion is the expansion of a power of a sum of three terms into monomials The expansion is given by ( a b c ) n = ∑ i j k = n i , j , k ( n i , j , k ) a i b j c k , {\displaystyle (abc)^ {n}=\sum _ {\stackrel {i,j,k} {ijk=n}} {n \choose i,j,k}\,a^ {i}\,b^ {\;\!j}\;\!c^ {k},}Let the literals a and b represent two terms in algebraic form The subtraction of b from a is written as a − b It is basically an algebraic expression and also a binomial The square of this expression is written as ( a − b) 2 in mathematical form and it is expanded as a 2 − 2 a b b 2 mathematically In mathematics, this algebraic identity is used as a formula and it is called in the following three ways

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