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In elementary algebra, the binomial theorem (or binomial expansion) describes the algebraic expansion of powers of a binomial.According to the theorem, it is possible to expand the polynomial (x + y) n into a sum involving terms of the form ax b y c, where the exponents b and c are nonnegative integers with b + c = n, and the coefficient a of each term is a specific positive integer depending ...
Polynomial expansion. In mathematics, an expansion of a product of sums expresses it as a sum of products by using the fact that multiplication distributes over addition. Expansion of a polynomial expression can be obtained by repeatedly replacing subexpressions that multiply two other subexpressions, at least one of which is an addition, by ...
Partial fraction decomposition. In algebra, the partial fraction decomposition or partial fraction expansion of a rational fraction (that is, a fraction such that the numerator and the denominator are both polynomials) is an operation that consists of expressing the fraction as a sum of a polynomial (possibly zero) and one or several fractions ...
The degree of the sum (or difference) of two polynomials is less than or equal to the greater of their degrees; that is, and . For example, the degree of is 2, and 2 ≤ max {3, 3}. The equality always holds when the degrees of the polynomials are different. For example, the degree of is 3, and 3 = max {3, 2}.
t. e. In mathematics, the Taylor series or Taylor expansion of a function is an infinite sum of terms that are expressed in terms of the function's derivatives at a single point. For most common functions, the function and the sum of its Taylor series are equal near this point.
It eventually surpassed PewDiePie to become the most-viewed YouTube channel of all time by February 16, 2017, [ 14 ] and currently maintains the lead with over 255 billion total views. T-Series has also had the most monthly views since 2016, [ 15 ][ 16 ] and received more than 2.8 billion views per month as of May 2019.
Extraneous and missing solutions. In mathematics, an extraneous solution (or spurious solution) is one which emerges from the process of solving a problem but is not a valid solution to it. [1] A missing solution is a valid one which is lost during the solution process. Both situations frequently result from performing operations that are not ...
The study — which appeared in BMC Nutrition & Metabolism — found that increasing dried fruit intake by about 1.3 pieces daily may lower the risk of type 2 diabetes by up to 60.8%.