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\ a = \sqrt{c^{2} b^{2}} \ Solve for the Length of Side b The length of side b is the square root of the squared hypotenuse minus the square of side a \ b = \sqrt{c^{2} a^{2}} \ Solve for Area A of the Right Triangle The area of a right triangle is side a multiplied by side b divided by 2= a 2 ab ac ba b 2 bc ca cb c 2 Adding like terms, the final formula (worth remembering) is (a b c) 2 = a 2 b 2 c 2 2ab 2bc 2acFirst, we can expand the first equation as (a b)2 = 9 a2 2ab b2 = 9 Next, we can expand the second equation as (a −b)2 = 49 a2 −2ab b2 = 49 Then, we can add the left side of each equation and the right side of each equation giving a2 2ab b2 a2 − 2ab b2 = 9 49 a2 a2 2ab −2ab b2 b2 = 58

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B 25 bomber-Discrete Data Sets Mean, Median and Mode Values Calculate arithmetic mean2 29 if a ib=0 wherei= p −1, then a= b=0 30 if a ib= x iy,wherei= p −1, then a= xand b= y 31 The roots of the quadratic equationax2bxc=0;a6= 0 are −b p b2 −4ac 2a The solution set of the equation is (−b p 2a −b− p 2a where = discriminant = b2 −4ac 32

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Free expand & simplify calculator Expand and simplify equations stepbystepSquare Formulas (a b) 2 = a 2 b 2 2ab (a − b) 2 = a 2 b 2 − 2ab a 2 − b 2 = (a − b) (a b) (x a) (x b) = x 2 (a b) x ab (a b c) 2 = a 2 b 2 c 2 2ab 2bc 2ca (a (−b) (−c)) 2 = a 2 (−b) 2 (−c) 2 2a (−b) 2 (−b) (−c) 2a (−c) (a – b – c) 2 = a 2 b 2 c 2 − 2ab 2bc − 2caHolds only in fields of characteristic 2, which if finite, must have 2^m elements, where m is a positive integer Also holds in the (infinite) field of rational functions over such a field

What does (ab)^2 and (ab)^2 equal?" You are squaring two different binomials When you square a binomial, you multiply it by itself (a b)^2 = (a b)(a b) = a(a) a(b) b(a) b(b) {used foil method} = a^2 ab ab b^2 {multiplied through} = a^2 2ab b^2 {combined like terms}I am currently working on spivak calculus 4th edition One of the problem asks the following Prove that if $0 < a < b$ $ a < \sqrt(ab) < (ab)/2 < b$Show that (AB)^2,(A^2B^2),(AB)^2 is an AP Ask questions, doubts, problems and we will help you menu myCBSEguide Courses CBSE Entrance Exam Competitive Exams ICSE & ISC Teacher Exams UP Board Uttarakhand Board Features Online Test Practice Homework Help Downloads CBSE Videos Courses

$\implies$ $(ab)^2 \,=\, a^2b^22ab$ Simplification The subtraction of two times product of two terms from the sum of the squares of the terms is simplified as the square of difference of the terms2ac2bc3ad3bd Factorization found (2c 3d) • (a b) Trying to factor a multi variable polynomial 11 Split 2ac 2cb 3ad 3bd into two 2termRelated Topics Mathematics Mathematical rules and laws numbers, areas, volumes, exponents, trigonometric functions and more ;

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Section 23 Key Point In general, detAdetB ̸= det( AB);(a − b) 2 = (a − b)(a − b) = a(a − b) − b(a − b) = a 2 − ab − ba b 2 = a 2 − 2ab b 2 Practice Exercise for Algebra Module on Expansion of (a ± b) 2 Algebra (x±a)(y±b) by FOILComplex Numbers Complex numbers are used in alternating current theory and in mechanical vector analysis;

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(ab) 2 = a 2 2ab b 2 (ab)(cd) = ac ad bc bd a 2 b 2 = (ab)(ab) (Difference of squares) a 3 b 3 = (a b)(a 2 ab b 2) (Sum and Difference of CubesSimplify (ab)^2(ab)^2 Simplify each term Tap for more steps Rewrite as Expand using the FOIL Method Tap for more steps Apply the distributive property Apply the distributive property Apply the distributive property Simplify and combine like terms Tap for more steps Simplify each term Tap for more stepsBy closure under addition, (ba)(ba)>0 Or, b^2a^2>0 Or, b^2>a^2 Or, a^2

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A review of the difference of squares pattern (ab)(ab)=a^2b^2, as well as other common patterns encountered while multiplying binomials, such as (ab)^2=a^22abb^2 Google Classroom Facebook Twitter(ab)^2 = a^2 2abb^2 this equation 1 (ab)^2 = a^2 2abb^2 this equation 2 (ab)^2 (ab)^2 = equation 1 equation 2 = a^2 2abb^2 (a^2 2abb^2)Simplify the Algebraic expression The square of sum of terms a and b is expanded as an algebraic expression a 2 a b b a b 2 According to commutative property, the product of a and b is equal to the product of b and a So, a b = b a ( a b) 2 = a 2 a b a b b 2

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Binomial Theorem (ab)1 = a b ( a b) 1 = a b (ab)2 = a2 2abb2 ( a b) 2 = a 2 2 a b b 2 (ab)3 = a3 3a2b 3ab2 b3 ( a b) 3 = a 3 3 a 2 b 3 a b 2 b 3 (ab)4 = a4 4a3b 6a2b2 4ab3 b4 ( a b) 4 = a 4 4 a 3 b 6 a 2 b 2 4 a b 3 b 4Thus the expansion for (a b) 6 is (a b) 6 = 1a 6 6a 5 b 15a 4 b 2 a 3 b 3 15a 2 b 4 6ab 5 1b 6 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 ourGeometrical proof of ab whole square formula with procedure to derive expansion of (ab)^2 identity is equal to a²2abb² in algebraic mathematics

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