👍 Correct answer to the question The identity (x^2 y^2)^2 = (x^2 y^2)^2 (2xy)^2 can be used to generate Pythagorean triples What Pythagorean triple could be generated using x = 8 and y = 3?Write a(x)/ b(x) in the form q(x) r(x)/ b(x), where a(x), b(x), q(x), and r(x) areYou can put this solution on YOUR website!
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The identity (x^2 y^2)^2=(x^2-y^2)^2 (2xy)^2 can be used
The identity (x^2 y^2)^2=(x^2-y^2)^2 (2xy)^2 can be used-Answer 2 📌📌📌 question The identity (x^2y^2)^2 = (x^2y^2)^2 (2xy)^2 can be used to generate pythagorean triples what pythagorean triple could be generated using x=8 and y=3 the answers to estudyassistantcom The identity (x^2 y^2)^2 = (x^2 – y^2)^2 (2xy)^2 can be used to generate Pythagorean triples What Pythagorean triple could be generated using x = 8 and y Skip to Content
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When adding and multiplying like terms students may initially confuse x x as x2 instead of 2x factors and can be used to factor polynomials of any power The degree of a polynomial will identity (x 2 y 2) 2 = (x 2 y 2) 2 (2xy) 2 can be used to(x – y) 2 = x 2 – 2xy y 2 LHS = RHS Hence, proved x 2 – y 2 = (x y) (x – y) By taking RHS and multiplying each term (x y) (x – y) = x 2 – xy xy – y 2 (x y) (x – y) = x 2 – y 2 Or x 2 – y 2 = (x y) (x – y) LHS = RHS Hence proved In the same way, you can prove the other above given algebraic identities Problems on Algebraic Identities Problem Solve (x 3) (x – 3) using algebraic identities Solution By the algebraic identity, x 2 How do you use Implicit differentiation find #x^2 2xy y^2 x=2# and to find an equation of the tangent line to the curve, at the point (1,2)?
1 6 x 2 4 y 2 9 z 2 1 6 x y 1 2 y z 2 4 x z Medium View solution Factorise 4 x 4 9 y 4 6 x 2 y 2 Easy View solution Factorise the following, using the identity a 2Write a(x)/ b(x) in the form q(x) r(x)/ b(x), where a(x), b(x), q(x), and r(x) are polynomials with the degree of r(x) less• See x4 – y4 as (x2)2 – (y2)2, thus recognizing it as a difference of squares that can be factored as (x2 – y2)(x2 y2) • In the equation x2 2x 1 y2 = 9, see an opportunity to rewrite the first three terms as (x1)2, thus recognizing the equation of a circle with radius 3 and center (−1, 0)
By using formula (xy)^2 = x^2 y^2 2xy we can solve this problem Now x^2 y^2 = (xy)^2 2xy Simply put the given values in the above equation & you will get the answer 28 The following identity can be used to find Pythagorean triples, where the expressions x2−y2, 2xy, and x2y2 represent the lengths of three sides of a right triangle;Believe me this can't be simplified It can be expanded and multiplied out (x^(2)2xyy)^2 becomes x^44 x^3 y4 x^2 y^22 x^2 y4 x y^2y^2 and then you still have to multiply by (xy) and that can become x^5(5 x2) x^3 y(8 x^26 x1) x y^2(2 x1)^2 y^3 or that can become
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PreAlgebra Simplify (2xy^22x^3x^2y) (2x^2y2xy^2y^3) (2xy2 2x3 − x2y) − (−2x2y 2xy2 − y3) ( 2 x y 2 2 x 3 x 2 y) ( 2 x 2 y 2 x y 2 y 3) Simplify each term Tap for more steps Apply the distributive propertyFor example, the polynomial identity (x^2 y^2)^2 = (x^2 – y^2)^2 (2xy)^2 can be used to generate Pythagorean triples I can prove polynomial identitiesAnswer to Verify the identity \bigtriangledown ^2 \vec \text v = \ grad \ div \vec \text v \ curl \ curl \vec \text v for the vector field \vec
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The identity (x^2 y^2)^2 = (x^2 y^2)^2 (2xy)^2 can be used to generate Pythagorean triples What Pythagorean triple could Mathematics, 0640 yo2lo15 The identity (x^2 y^2)^2 = (x^2 y^2)^2 (2xy)^2 can be used to generate Pythagorean triples$\psi = x^2(y2)^2\lambda(x^2y^21)$ Establish Lagrange Equations $$\psi_x = 2x\lambda(2x)=0 $$ $$\psi_y = 2y4\lambda(2y)=0$$ $$\psi_\lambda = x^2y^21=0$$The polynomial identity (x2 y2)2 = (x2 – y2)2 (2xy)2 can be used to generate Pythagorean triples D Rewrite rational expressions AAPRD6 Rewrite simple rational expressions in different forms;
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An algebraic identity is an equality that holds for any values of its variables For example, the identity ( x y) 2 = x 2 2 x y y 2 (xy)^2 = x^2 2xy y^2 (x y)2 = x2 2xyy2 holds for all values of x x x and y y y Since an identity holds for all values of its variables, it is possible to substitute instances of one side of theFor example, the polynomial identity (x 2 y 2) 2 = (x 2 y 2) 2 (2xy) 2 can be used to generate Pythagorean triples Authors National Governors Association Center for Best Practices, Council of Chief State School Officers Title CCSSMathContentHSAAPRC4 Prove Polynomial Identities And Use Them To DescribeFor example, the polynomial identity (x^2 y^2 )^ 2 = (x^2 – y^ 2 )^ 2 (2xy)^2 can be used to generate Pythagorean triples AAPRC5 () Know and apply the Binomial Theorem for the expansion of (x y)^n in powers of x and y for a positive integer n, where x and y are any numbers, with coefficients determined for example by Pascal's Triangle
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The Pythagorean triple Identity is (x 2 y 2) 2 = (x 2 y 2) 2 (2xy) 2, where c = x 2 y 2, a = x 2 y 2, and b = 2xy With x = 3 and y = 5 a = 3 2 5 2 = 16, (this is 16, by the rules x should be greater than y (x > y), in this case √(x 2 y 2) 2 = a) b = 2*3*5 = 30 c = 3 2 5 2For cases where equality is shown using numerical values, (name) will use algebraic operations (eg distributive property, collecting like terms) to prove that the polynomials are equivalentMAFS912AAPR22 In this video, students will use the Polynomial Remainder Theorem to determine whether a linear expression is a factor of a polynomial expression • Internet connection • Speakers/headphones • Computer • Scientific calculator (if necessary) Dividing Polynomials • MAFS912AAPR22 This tutorial can be used to help
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For ex ample, the polyno mial identity (x2 y2)2 = (x2 – y2)2 (2xy)2 can be used to generate Pythagorean triples Interpret functions that arise in applications in terms of the context MGSE912FIF4 Using tables, graphs, and verbal descriptions, interpret the key characteristics of a function which models theCan solve it using a simple identity Let's get to the point x y = ?X and y are positive integers;
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Identities V Last updated at by Teachoo Identity V is (a b c) 2 = a 2 b 2 c 2 2ab 2bc 2ca Let us prove it Proof (a b c) 2 = ( (a b) c) 2 Using (x y) 2 = x 2 y 2 2xyX 2 y 2 2 x 2 y = 1 x 2 − y 2 − 2 x − 2 y = 1 Complete the square for x 2 2 x x 2 − 2 x Tap for more steps Use the form a x 2 b x c a x 2 b x c, to find the values of a a, b b, and c c a = 1, b = 2, c = 0 a = 1, b = − 2, c = 0 Consider the vertex form of a parabolaAnd x>y Calculus Find the four second partial derivatives and evaluate each at the given point
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X and y are positive integers;Write a(x)/b(x) in the form q(x)By (date), when given a polynomial identity (eg *x^2 y^2 = (x y) (x y)*), (name) will substitute given values (eg *x* = 6 and *y* = 2) and check if both sides of theidentity are equal;
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For example, the polynomial identity (x2 y2)2 = (x2 – y2)2 (2xy)2 can be used to generate Pythagorean triples D Rewrite rational expressions 6 Rewrite simple rational expressions in different forms;In this lesson you will learn to generate a Pythagorean Triple by using the identity (x^2 y^2)^2 (2xy)^2 = (x^2 y^2)^2 Please wait while your changes are saved Create your free accountIf xy = 30 , x^2 y^2 = 61 Using the identity (xy)^2 = x^2 y^2 2xy => (xy)^2 = 61 2(30) => (xy)^2 = 61 60 => (xy)^2 = 1 => (xy) = 1 Therfore the value of xy i
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Identity (x^2 y^2)^2 = (x^2 – y^2)^2 (2xy)^2 can be used to generate Pythagorean triples A AREI06 Solve systems of equations Solve systems of linear equations exactly and approximately (eg, with graphs), focusing on pairs of linear equations in two variables 22b Solve systems of linear equations andProve polynomial identities and use them to describe numerical relationships For example, the polynomial identity (x 2 y 2) 2 = (x 2 – y 2) 2 (2xy) 2 can be used The following identity can be used to find Pythagorean triples, where the expressions x2−y2, 2xy, and x2y2 represent the lengths of three sides of a right triangle;
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The quadratic formula gives two solutions, one when ± is addition and one when it is subtraction y^ {2}2xyx^ {2}=0 y 2 2 x y x 2 = 0 This equation is in standard form ax^ {2}bxc=0 Substitute 1 for a, 2x for b, and x^ {2} for c in the quadratic formula, \frac {b±\sqrt {b^ {2Use the distributive law to explain why x2 – y2 = (x – y)(x y) for any two numbers x and y Derive the identity (x – y)2 = x2 – 2xy y2 from (x y)2 = x2 2xy y2 by replacing y by –y Use an identity to explain the pattern 22 – 12 = 3 32 – 22 = 5 42 – 32 = 7 52 – 42 = 9 Answer (n 1)2 n2 = 2n 1 for any whole number nFor example, the polynomial identity (x 2 y 2) 2 = (x 2 – y 2) 2 (2xy) 2 can be used to generate Pythagorean triples With the increase in technology and this huge new thing called the Internet, identity theft has become a worldwide problem
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Calculus Basic Differentiation Rules Implicit DifferentiationFor example, the polynomial identity (x 2 y 2) 2 = (x 2 – y 2) 2 (2xy) 2 can be used to generate Pythagorean triples Rewrite rational expressions AAPRD6Students will prove the polynomial identity ( x^2 y^2 )^2 ( 2xy )^2 = ( x^2 y^2 )^2 and use it to generate Pythagorean triples Use this activity as independent/partner practice or implement it as guided notes and practice for students in need of extra support
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Correct answer The identity (x^2 y^2)^2 = (x^2 y^2)^2 (2xy)^2 can be used to generate Pythagorean triples What Pythagorean triple could be genFor example, the polynomial identity (x2 y2)2 = (x2 y2)2 (2xy)2 can be used to generate Pythagorean triples AAPRD Rewrite rational expressions AAPRD6 Rewrite simple rational expressions in different forms;Using identity, (xyz)2 2= x y2z22xy2yz2zx We can say that, x 2 y 2 z 2xy2yz2zx = (xyz) 2 4x 2 9y 16z 2 12xy–24yz–16xz = (2x) 2 (3y) 2 (−4z)(2×2x×3y)(2×3y×−4z)(2×−4z×2x)
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The polynomial identity (x2 y2)2 = (x2 – y2)2 (2xy)2 can be used to generate Pythagorean triples SE/TE CB 318 AAPR5 () Know and apply the Binomial Theorem for the expansion of (x y)n in powers of x and y for a positive integer n, where x y are any numbers, with coefficients determined for example by Pascal's Triangle SE/TEAnd x>y (x2−y2)2(2xy)2=(x2y2)2 If the sides of a right triangle are 57, 176, and 185, what are the values of x and y?2) ASSE2 Use the structure of an expression to identify ways to rewrite it For example, see x4 – y 4 as (x2)2 – (y2)2, thus recognizing it as a difference of squares that can be factored as (x2 – y 2)(x2 y2) 3) ASS Choose and produce an equivalent form of an expression to reveal and explain properties
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Prove polynomial identities and use them to describe numerical relationships For example, the polynomial identity (x 2 y 2) 2 = (x 2 –y 2) 2 (2xy) 2 can be used to generate Pythagorean triples WORKSHEETS RegentsPolynomial Identities AII 11 TST PDF DOC TNS PracticePolynomial Identities sum/difference of cubes 10 WS PDF1 See answer ans is X^2Y^2 = (XY)^22xy AryaBandal is waiting for your help Add your answer and earn points pmtibrahim18pmtibrahim18 x2 y2 can be written as (xy)2 this is in the form of (a b)2 = a2 2ab b2 so the above can be written as x2 2xy y2Use the identity (x^2y^2)^2=(x^2−y^2)^2(2xy)^2 to determine the sum of the squares of two numbers if the difference of the squares of the numbers is 5 and the product of the numbers is
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HSAAPRC4 Prove polynomial identities and use them to describe numerical relationships For example, the polynomial identity (x 2 y 2 ) 2 = (x 2 y 2 ) 2 (2xy) 2 can be used to generate Pythagorean triplesFor example, the polynomial identity (x 2 y 2) 2 = (x 2 – y 2) 2 (2xy) 2 can be used to generate Pythagorean triples Suggested Learning Targets Understand that polynomial identities include but are not limited to the product of the sum and difference of two terms, the difference of two squares, the sum and difference of two cubes, the
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