difference of two squares is one squared number (the number multiplied by itself) subtracted from another squared number. Every difference of squares...

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...

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...

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...

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,...

two-square identity Candido's identity Cassini and Catalan identities Degen's eight-square identity Difference of two squares Euler's four-square identity...

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}...

the South Korean series Difference of two squares, a mathematical term Dot-S, a toy released in Japan Dot (disambiguation) Two dots (disambiguation) Three...

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 ) (...

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...

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)...

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}}...

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...

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...

{\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...

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...

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...

Difference in differences (DID or DD) is a statistical technique used in econometrics and quantitative research in the social sciences that attempts to...

factorization algorithm: algebraic factors of binomial numbers (e.g. difference of two squares and sum of two cubes), which depend on the exponent, and...

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...

method Euler's factorization method Special number field sieve Difference of two squares A general-purpose factoring algorithm, also known as a Category...

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...

{\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...

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...

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...

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...

Series, Golden Ratio, properties of Square, Triangle, Cube, Centred Hexagon and Tetrahedral numbers, "difference of two squares", number superstitions, prime...

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...

{\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...

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...