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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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Definition The longest side of the triangle is called the "hypotenuse", so the formal definition isSee below mathbf A times mathbf B = mathbf A mathbf B sin alpha \ hat (mathbf n) mathbf A * mathbf B = mathbf A mathbf B cos alpha implies mathbf A timesFor a square b square watch http//youtube/24gWbMSEVVwLearn how a minus b whole square can be explained using geometrical drawingsFor more such videos v
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If a/b =2 then what will be 4b/a Look at the equation, a/b=2 so therefore a = 2b Now that we know the value of a, that is, 2b, In this equation, 4b/a, All we have to do is substitute the values of a (2b) since a = 2b, then, 4b/2b By normal division, you'll get 2 as the answerSolution for X (ab2)=100 equation Simplifying X (a b 2) = 100 Reorder the terms X (2 a b) = 100 Remove parenthesis around (2 a b) X 2 a b = 100 Reorder the terms 2 X a b = 100 Solving 2 X a b = 100 Solving for variable 'X'(a−b) 2 = a 2 − 2ab b 2 If you want to see why, then look at how the (a−b) 2 square is equal to the big a 2 square minus the other rectangles (a−b) 2 = a 2 − 2b(a−b) − b 2
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No, because matrix multiplication is not commutative in general, so (AB)(AB) = A^2ABBAB^2 is not always equal to A^2B^2 Since matrix multiplication is not commutative in general, take any two matrices A, B such that AB != BA11 Evaluate (ab) 2 = a 22abb 2 Step 2 Pulling out like terms 21 Pull out like factors 2ab 2b 2 = 2b • (a b) Equation at the end of step 2 2b • (a b) = 0 Step 3 Theory Roots of a product 31 A product of several terms equals zero When a product of two or more terms equals zero, then at least one of the terms must(a b) 2 This can also be written as = (a b) (a b) Multiply as we do multiplication of two binomials and we get = a(a b) b(a b) = a 2 ab ab b 2 Add like terms and we get = a 2 2ab b 2 Rearrange the terms and we get = a 2 b 2 2ab Hence, in this way we obtain the identity ie (a b) 2 = a 2 b 2 2ab
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We answer the question whether for any square matrices A and B we have (AB)(AB)=A^2B^2 like numbers We actually give a counter example for the statement$\implies$ $(ab)^2 \,=\, a^2b^22ab$ 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 termsSimplify (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 steps
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And you should be extremely careful not to assume anything about the determinant of a sum Nerdy Sidenote One large vein of current research in linear algebra deals with this question of how detA and detB relate to det(AB)One way to handle the question is this instead of trying to find the value forProbably the answer would be yes and is simple Everybody knows it and when you multiply (ab) with (ab) you will get a plus b whole square (ab) * (ab) = a 2 ab ba b 2 = a 2 2ab b 2 But how did this equation a plus b whole square became generalized Let's prove this formula geometrically( Please refer to the pictures on the side)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} (a b)^2 = (a b) (a b) = a (a) a (b) b (a) b (b) {used foil method}
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And that can be produced by the difference of squares formula (ab) (a−b) = a 2 − b 2 Like this ("a" is 2x, and "b" is 3) (2x3) (2x−3) = (2x) 2 − (3) 2 = 4x 2 − 9 So the answer is that we can multiply (2x3) and (2x−3) to get 4x2 − 9A and b are the other two sides ;B) b² = a ² 2 a b b ² In woorden Het kwadraat van een verschil is de som van het kwadraat van de eerste term, het tegengestelde van het dubbel van het product van de twee termen en het kwadraat van de tweede term
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First, multiply each side of the equation by #color(red)(2)# to eliminate the fraction while keeping the equation balanced #color(red)(2) xx A= color(red)(2) xx h/2There is stated that the thesis for the proof is short multiplication formula $$(2)\space\space\space\space\space\space\space\space\space(ab)^2=a^22abb^2$$ Substracting from the short multiplication $(2)$ formula $4ab$ and using square root yields the proof by implicationA 2 b 2 = (ab) (ab) (Difference of squares) a 3 b 3 = (a b) (a 2 ab b 2) (Sum and Difference of Cubes) x 2 (ab)x AB = (x a) (x b) if ax 2 bx c = 0 then x = ( b (b 2 4ac) ) / 2a (Quadratic Formula) Contact us Advertising & Sponsorship Partnership Link to us © 0005 Mathcom
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A 2 b 2 = c 2 Note c is the longest side of the triangle;Square Formulas(a b)2= a2 b2 2ab(a − b)2= a2 b2− 2aba2− b2= (a − b) (a b)(x a) (x b) = x2 (a b) x ab(a b c)2= a2 b2 c2 2ab 2bc 2caA 2 b 2 = (a b) 2 = a 2 2 a b b 2 a^2 b^2 = (ab)^2 = a^2 2ab b^2 a 2 b 2 = (a b) 2 = a 2 2 a b b 2 This is clearly not an identity since 2 a b 2ab 2 a b is not always 0 Thus, we can conclude that this is an identity if and only if 2 a b = 0 2ab = 0 2 a b = 0 Proof 3 Geometric interpretation We can also look at this geometrically and immediately see that it is false
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Equations Tiger Algebra gives you not only the answers, but also the complete step by step method for solving your equations (ab)^2(ab)^2 so that you understand betterThere are various student are search formula of (ab)^3 and a^3b^3 Now I am going to explain everything below You can check and revert back if you like you can also check cube formula in algebra formula sheet a2 – b2 = (a – b)(a b) (ab)2 = a2 2ab b2 a2 b2 = (a –For a square b square watch http//youtube/24gWbMSEVVwLearn how a minus b whole square can be explained using geometrical drawingsFor more such videos v
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For a square b square watch http//youtube/24gWbMSEVVwLearn how a minus b whole square can be explained using geometrical drawingsFor more such videos vRelated Documents Binomial Theorem Binomial theorem for positive integers;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 (a – b – c) 2 = a 2 b 2 c 2 – 2ab 2bc – 2ca
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Holds 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
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