• difference of two squares is one squared number (the number multiplied by itself) subtracted from another squared number. Every difference of squares...
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  • Thumbnail for Factorization
    factorization of x 4 + 1. {\displaystyle x^{4}+1.} If one introduces the non-real square root of –1, commonly denoted i, then one has a difference of squares x 4...
    42 KB (7,863 words) - 13:39, 5 June 2025
  • the representation of an odd integer as the difference of two squares: N = a 2 − b 2 . {\displaystyle N=a^{2}-b^{2}.} That difference is algebraically factorable...
    16 KB (3,308 words) - 04:22, 13 June 2025
  • Thumbnail for Sum of two cubes
    15^{3}+9^{3}} or − 12 3 + 18 3 {\displaystyle -12^{3}+18^{3}} Difference of two squares Binomial number Sophie Germain's identity Aurifeuillean factorization...
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  • Thumbnail for Square number
    less than a square (3 = 22 − 1). More generally, the difference of the squares of two numbers is the product of their sum and their difference. That is,...
    18 KB (2,540 words) - 21:45, 22 June 2025
  • two-square identity Candido's identity Cassini and Catalan identities Degen's eight-square identity Difference of two squares Euler's four-square identity...
    2 KB (175 words) - 11:10, 21 June 2024
  • In additive number theory, Fermat's theorem on sums of two squares states that an odd prime p can be expressed as: p = x 2 + y 2 , {\displaystyle p=x^{2}+y^{2}...
    36 KB (6,609 words) - 01:55, 26 May 2025
  • the South Korean series Difference of two squares, a mathematical term Dot-S, a toy released in Japan Dot (disambiguation) Two dots (disambiguation) Three...
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  • 4 + 36 x 2 + 324 ) − 36 x 2 = ( x 2 + 18 ) 2 − ( 6 x ) 2 = a difference of two squares = ( x 2 + 18 + 6 x ) ( x 2 + 18 − 6 x ) = ( x 2 + 6 x + 18 ) (...
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  • Thumbnail for Least squares
    justification for the method of least squares and the normal distribution. In 1822, Gauss was able to state that the least-squares approach to regression analysis...
    36 KB (5,243 words) - 23:15, 19 June 2025
  • Thumbnail for Square root
    positive definite. Each element of an integral domain has no more than 2 square roots. The difference of two squares identity u2 − v2 = (u − v)(u + v)...
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  • the smallest natural number that can be expressed as the difference of two nonzero squares in more than three ways: 10 2 − 2 2 {\displaystyle 10^{2}-2^{2}}...
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  • Thumbnail for Square (algebra)
    discussed above Degen's eight-square identity, related to octonions in the same way Difference of two squares Euler's four-square identity, related to quaternions...
    15 KB (1,990 words) - 03:13, 22 June 2025
  • mean square deviation (RMSD) or root mean square error (RMSE) is either one of two closely related and frequently used measures of the differences between...
    11 KB (1,622 words) - 20:57, 23 June 2025
  • {\displaystyle 2x^{3}+7} The binomial x2 − y2, the difference of two squares, can be factored as the product of two other binomials: x 2 − y 2 = ( x − y ) ( x...
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  • Thumbnail for Magic square
    magic squares, while merely passing on the finished diagrams of larger squares. He gives a magic square of order 3, two squares for each order of 4 to...
    272 KB (21,802 words) - 12:40, 22 July 2025
  • Least squares For the "sum of squared differences", see Mean squared error For the "sum of squared error", see Residual sum of squares For the "sum of squares...
    4 KB (704 words) - 22:13, 18 November 2023
  • Difference in differences (DID or DD) is a statistical technique used in econometrics and quantitative research in the social sciences that attempts to...
    21 KB (3,180 words) - 14:48, 24 July 2025
  • factorization algorithm: algebraic factors of binomial numbers (e.g. difference of two squares and sum of two cubes), which depend on the exponent, and...
    10 KB (995 words) - 12:02, 10 April 2025
  • square, the quadratic expression can be reduced to a sum of two squares then the equation defines an ellipse, whereas if it reduces to a difference of...
    9 KB (1,495 words) - 01:29, 3 November 2024
  • method Euler's factorization method Special number field sieve Difference of two squares A general-purpose factoring algorithm, also known as a Category...
    25 KB (2,977 words) - 21:02, 19 June 2025
  • Thumbnail for Quartic equation
    of folded perfect squares, one on each side of the equation. The two perfect squares balance each other. If two squares are equal, then the sides of the...
    32 KB (6,917 words) - 14:06, 19 July 2025
  • {\displaystyle \cos ^{2}\theta +\sin ^{2}\theta } as the complex difference of two squares, 1 = e i θ e − i θ = ( cos ⁡ θ + i sin ⁡ θ ) ( cos ⁡ θ − i sin...
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  • unobserved quantity) measures the average of the squares of the errors—that is, the average squared difference between the estimated values and the true value...
    24 KB (3,861 words) - 12:45, 11 May 2025
  • square with area equal either to the sum or to the difference of two given squares. Both constructions proceed by letting the largest of the squares be...
    24 KB (2,965 words) - 19:09, 1 June 2025
  • making it more easily solvable. In algebra, an example of an identity is the difference of two squares: x 2 − y 2 = ( x + y ) ( x − y ) {\displaystyle...
    32 KB (4,249 words) - 15:11, 18 July 2025
  • Murderous Maths (category Series of non-fiction books)
    Series, Golden Ratio, properties of Square, Triangle, Cube, Centred Hexagon and Tetrahedral numbers, "difference of two squares", number superstitions, prime...
    15 KB (1,865 words) - 08:58, 15 June 2025
  • In mathematics, a square-difference-free set is a set of natural numbers, no two of which differ by a square number. Hillel Furstenberg and András Sárközy...
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  • {\displaystyle {\sqrt {2}}\mp {\sqrt {3}}\,} and applying the difference of two squares identity, which here will yield −1. To get this result, the entire...
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  • x^{4}+4y^{4}=(x^{2}+2y^{2})^{2}-4(xy)^{2},} a difference of two squares, from which Germain's identity follows. The inaccurate attribution of this identity to Germain was...
    6 KB (869 words) - 14:19, 27 August 2024