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Fourth powers are also formed by multiplying a number by its cube. Furthermore, they are squares of squares. Some people refer to n 4 as n “ tesseracted ”, “ hypercubed ”, “ zenzizenzic ”, “ biquadrate ” or “ supercubed ” instead of “to the power of 4”.
In arithmetic and algebra, the cube of a number n is its third power, that is, the result of multiplying three instances of n together. The cube of a number or any other mathematical expression is denoted by a superscript 3, for example 2 3 = 8 or (x + 1) 3. The cube is also the number multiplied by its square: n 3 = n × n 2 = n × n × n.
The polynomial () (+) is a cubic polynomial: after multiplying out and collecting terms of the same degree, it becomes + +, with highest exponent 3.. The polynomial (+ +) + (+ + +) is a quintic polynomial: upon combining like terms, the two terms of degree 8 cancel, leaving + + + +, with highest exponent 5.
In the 9th century, the Persian mathematician Al-Khwarizmi used the terms مَال (māl, "possessions", "property") for a square—the Muslims, "like most mathematicians of those and earlier times, thought of a squared number as a depiction of an area, especially of land, hence property" [9] —and كَعْبَة (Kaʿbah, "cube") for a cube ...
The square of an integer may also be called a square number or a perfect square. In algebra, the operation of squaring is often generalized to polynomials, other expressions, or values in systems of mathematical values other than the numbers. For instance, the square of the linear polynomial x + 1 is the quadratic polynomial (x + 1) 2 = x 2 ...
"Completing the square" consists to remark that the two first terms of a quadratic polynomial are also the first terms of the square of a linear polynomial, and to use this for expressing the quadratic polynomial as the sum of a square and a constant. Completing the cube is a similar technique that allows to transform a cubic polynomial into a ...
After this change of variable, the new graph is the mirror image of the previous one, with respect of the y-axis. Then, the change of variable x = x 1 – b / 3a provides a function of the form = + +. This corresponds to a translation parallel to the x-axis.
The number of cube roots of a number depends on the number system that is considered. Every nonzero real number x has exactly one real cube root that is denoted and called the real cube root of x or simply the cube root of x in contexts where complex numbers are not considered.