√完了しました！ (a+b)^3 161615-A b 3088
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)(a + b)(a +b) =(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,
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A b 3088
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(a – b – c) 2 = a 2 + b 2 + c 2 – 2ab + 2bc – 2ca#(a-b)^3 = a^3 + 3a^2(-b)^1 + 3a(-b)^2+(-b)^3# #= a^3 - 3a^2b +3ab^2 -b^3#6a2b Step by step solution :
(a – b)3 = a3 – 3a2b + 3ab2 – b3(a – b) 3 = (a – b)Compute answers using Wolfram's breakthrough technology & knowledgebase, relied on by millions of students & professionals
A³ - 3a²b + 3ab² - b³(a – b) 3 = (a – b) a 2 + b 2 -2ab (a – b) 3 = a a 2 + b 2 -2ab -b a 2 + b 2 -2ab (a – b) 3 = a 3 + ab 2 – 2a 2 b -ba 2 -b 3 + 2ab 2(a+b)^3+(a-b)^3 = (b+a)^3-(b-a)^3 = 2a(3b^2+a^2)
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= (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 + b3(a + b – c) 2 = a 2 + b 2 + c 2 + 2ab – 2bc – 2ca
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(((a + b)3) - ((a - b)3)) - 2b3 Step 2 :Final result :(a – b + c) 2 = a 2 + b 2 + c 2 – 2ab – 2bc + 2ca(a – b) 3 can be written as
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=2b(sqrt(3)a+ib)(sqrt(3)a-ib) Notice also that:= (a2 + 2ab +b2)(a +b) =(a – b) 2
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#(a-b)^3 = (a +(-b))^3# Substitute into the Binomial expansion formula, let #x = a# and #y = -b#:= (a2 + ab + ab +b2)(a +b) == a3 +a2b +2a2b +2ab2 +ab2 +b3 =
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(a + b + c) 2 = a 2 + b 2 + c 2 + 2ab + 2bc + 2ca(a – b) 3 = a 3 – 3a 2 b + 3ab 2 – b 36a2b Processing ends successfully
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MATHEMATICAL FORMULAE Algebra 1Step 1 :Equation at the end of step 1 :(a+b)^3-(a-b)^3 = (a^3+3a^2b+3ab^2+b^3)-(a^3-3a^2b+3ab^2-b^3) = 6a^2b+2b^3 =2b(3a^2+b^2) If you are allowed complex coefficients this can be broken down into linear factors:
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It's easy to prove:(a + b)3 = a3 +3a2b +3ab2 +b3For math, science, nutrition, history, geography, engineering, mathematics, linguistics, sports, finance, music… Wolfram|Alpha brings expert-level knowledge and
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