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Algebra is the branch of mathematics that studies certain abstract systems, known as algebraic structures, and the manipulation of expressions within those systems. It is a generalization of arithmetic that introduces variables and algebraic operations other than the standard arithmetic operations, such as addition and multiplication.
A mathematical exercise is a routine application of algebra or other mathematics to a stated challenge. Mathematics teachers assign mathematical exercises to develop the skills of their students. Early exercises deal with addition, subtraction, multiplication, and division of integers.
The order of operations, that is, the order in which the operations in an expression are usually performed, results from a convention adopted throughout mathematics, science, technology and many computer programming languages.
Algebraic geometry is a branch of mathematics which uses abstract algebraic techniques, mainly from commutative algebra, to solve geometrical problems. Classically, it studies zeros of multivariate polynomials; the modern approach generalizes this in a few different aspects.
A Boolean algebra can be interpreted either as a special kind of ring (a Boolean ring) or a special kind of distributive lattice (a Boolean lattice). Each interpretation is responsible for different distributive laws in the Boolean algebra. Similar structures without distributive laws are near-rings and near-fields instead of rings and division ...
Mathematically, the ability to break up a multiplication in this way is known as the distributive law, which can be expressed in algebra as the property that a(b+c) = ab + ac. The grid method uses the distributive property twice to expand the product, once for the horizontal factor, and once for the vertical factor.
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