WebAlgebra Simplify (a+b) (a^2-ab+b^2) (a + b) (a2 − ab + b2) ( a + b) ( a 2 - a b + b 2) Expand (a+b)(a2 −ab+b2) ( a + b) ( a 2 - a b + b 2) by multiplying each term in the first expression by each term in the second expression. a⋅a2 + a(−ab)+ab2 +ba2 +b(−ab)+b⋅b2 a ⋅ a 2 + a ( - a b) + a b 2 + b a 2 + b ( - a b) + b ⋅ b 2 Simplify terms. WebThe a^2 + b^2 formula is used to calculate the sum of two or more squares in an expression. Thus, a sum of squares formula or a^2 + b^2 formula can be expressed as: a 2 + b 2 = (a +b) 2 - 2ab. Also, a 2 + b 2 = (a - b) 2 + 2ab. where, a, b = arbitrary numbers. Let a and b be the two numbers, the squares of a and b are a 2 and b 2.
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WebBest answer The given numbers are (a-b)2, (a2 +b2) and (a2 +b2). Since each term differs from its preceding term by a constant, therefore, the given numbers are in AP. ← Prev … WebShow 2 2 (a, b)(a2, b2) = (a3, a2b, ab2, b3) [by basic gcd laws - see Remark below] = (a, b)3 Thus (a2, b2) = (a, b)2 by cancelling (a, b) ≠ 0. [ See here for the cubic analog] Or: Gauss's Lemma (GL) yields a slick proof. Let C(f) denote the content of a polynomial, i.e. the gcd of its coefficients. Then GL ⇒ C(fg)GL = C(f) C(g) so
WebBy squaring $1=ax+by$ both sides, I get, $1=(ax)^2+2(ax)(by)+(by)^2$, but this doesn't help my proof. Stack Exchange Network Stack Exchange network consists of 181 Q&A communities including Stack Overflow , the largest, most trusted online community for developers to learn, share their knowledge, and build their careers. Web(a) Let P(B1∩B2)>0, and A1∪A2⊂B1∩B2. Then show that. P(A1 B1).P(A2 B2)=P(A1 B2).P(A2 B1). (b) Let A and B1 be independent; similarly, let A and B2 be independent. Show that in this case, A and B1∪B2 are independent if and only if A and B1∩B2 are independent. (c) Given P(A) = 0.42,P(B) = 0.25, and P(A∩B) = 0.17, find …
WebIf a, b, c and d are in G.P. show that (a 2+b 2+c 2)(b 2+c 2+d 2)=(ab+bc+cd) 2 Hard Solution Verified by Toppr Taking LHS (a 2+b 2+c 2)(b 2+c 2+d 2) putting values b=ar,c=ar 2,d=ar 3 (a 2+(ar) 2+(ar 2) 2)((ar) 2+(ar 2) 2+(ar 3) 2) =a 2(1+r 2+r 4)a 2(r 2+r 4+r 6) =a 4r 2(1+r 2+r 4) 2 RHS =(ab+bc+cd) 2 =(a×ar+ar×ar 2+ar 2×ar 3) 2 WebX, Y, A, B are the most commonly used letters that represent algebraic problems and equations. Important Formulas in Algebra Here is a list of Algebraic formulas – a 2 – b 2 = (a – b) (a + b) (a + b) 2 = a 2 + 2ab + b 2 a 2 + b 2 = (a + b) 2 – 2ab (a – b) 2 = a 2 – 2ab + b 2 (a + b + c) 2 = a 2 + b 2 + c 2 + 2ab + 2bc + 2ca
WebIf A happens, it excludes B from happening, and vice-versa. A B Ω If Aand B are mutually exclusive, P(A∪B) = P(A)+ P(B). For all other Aand B, P(A∪B) = P(A)+ P(B)−P(A∩B). Definition: Any number of events B1,B2,...,B kare mutually exclusive if every pair of the events is mutually exclusive: ie. B i∩B j= ∅for alli,jwithi6= j. Ω B1B2B3
WebMedium Solution Verified by Toppr Correct option is A) Given, 2a 2+2b 2=a 2+2ab+b 2. We know, (a+b) 2=a 2+2ab+b 2 and (a−b) 2=a 2−2ab+b 2. The value of 2(a 2+b 2)=(a+b) 2 is … natural homemade acne spot treatmentWebFree math problem solver answers your algebra, geometry, trigonometry, calculus, and statistics homework questions with step-by-step explanations, just like a math tutor. maricopa county restraining order formsWebMar 22, 2024 · Example 23, If a, b, c, d and p are different real numbers such that (a2 + b2 + c2)p2 2(ab + bc + cd) p + (b2 + c2 + d2) 0, then show that a, b, c and d are in G.P. … natural homemade bug spraysWebProve the law of cosines c2 = a2+b2-2 a b cos C for a triangle gradevalue 64 subscribers Subscribe 43 10K views 8 years ago This video shows how to prove the law of cosines c2 = a2+... maricopa county ride alongWebThis question already has answers here: For all square matrices A and B of the same size, it is true that ( A + B) 2 = A 2 + 2 A B + B 2? (2 answers) Closed 6 years ago. Hello i just need some help with proving that ( A + B) 2 = A 2 + 2 A B + B 2 holds for commutative matrices. Maybe by induction ? linear-algebra matrices Share Cite Follow maricopa county road construction projectsWebJun 10, 2024 · Show that (a - b)2, (a2 +b2) and (a + b)2 are in Ap See answer Advertisement Suchetsadekar The resulting series is an A.P. with common difference = 2ab are u sure about this solution Advertisement Advertisement natural homemade cough syrupWebFor all square matrices A and B of the same size, it is true that ( A + B) 2 = A 2 + 2 A B + B 2? (2 answers) Closed 6 years ago. Assume that A and B are both n × n matrices, how would … natural homemade face scrub for oily skin