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Zero Product Property - Explanation, Examples, and FAQs.Zero-product property - Wikipedia |
What is zero property. Zero-product property
So we can say that the multiplication of two non zero real numbers can never be zero. It is usually used in the solution of algebraic equations.
An algebraic expression is any expression that involves any variable. An algebraic equation is an algebraic expression that can be equated to zero. While we study mathematics by the use of symbols or variables for expressing different principles and formulas. When we equate an algebraic expression to zero then we solve the equation to find the value of the variable which will make the value of the expression zero. For this, we have to understand that the product of any number or expression is zero.
Algebraic equations and algebraic expressions play a very major role in science and Maths. All the advanced concepts in these fields depend on the very basic concept of algebra. The whole branch of theoretical physics is based on solutions of algebraic equations only. Many important discoveries in science including many groundbreaking ones are done by simply solving algebraic equations.
The famous theory of relativity is also found this way by solving an algebraic equation. While solving any algebraic equation we use the method of breaking the expression into simple multiplication of zeros. Zeros is a simple algebraic equation where the value of the variable can be found easily by equating the expression with zero. The zero product property definition in algebra states that the product of two nonzero elements is nonzero. In other words, this assertion:.
The zero product property is also known as the zero multiplication property, the null factor law, the nonexistence of nontrivial zero divisors, the zero product rule, or one of the two zero factor properties. The zero product rule is satisfied by all number systems including rational numbers, integers, real numbers, and complex numbers.
In general, a domain is a ring that satisfies the zero property. The figure above depicts a multiplication problem where there are 5 groups, each containing 3 groups of objects. The figure also depicts 5 groups that contain 0 objects, and a blank space to represent there being 0 groups of 3 objects. It is worth noting that even though division is the inverse operation of multiplication, it does not share a similar zero property.
Dividing by 0 does not result in 0, as in multiplication. In fact, it is not possible to divide any number by 0. The zero property of multiplication is one of a number of other multiplication properties such as the commutative, associative, distributive, and identity properties of multiplication. Learning the various properties of multiplication and other operations is important for building a foundation that enables a student to work with more complex mathematical concepts.
Particularly in algebra , knowing number properties enables us to simplify and solve a wide variety of algebraic equations.
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