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In algebra, real numbers have a number of properties that enable us to simplify and solve mathematical problems. Its density property for example, implies that there is always another real number that exists between any two real numbers given. For example, between 9.1 and 9.2, there are 9.11, 9.12, 9.13 and so forth. Its identity property says that any number added to zero is equal to itself. There are a number of other properties that real numbers have including distributive, commutative, reflexive and symmetric among others. They all serve the same purpose of helping us in problem solving.
For easier computation it is always important to cluster like terms together. In more complex expressions, the like terms must have the same variable raised to the same exponent.
During the simplification of the given expressions, properties of real numbers will be utilized and identified. The mathematical workings will be aligned on the left while the right side will discuss the properties used.
2a(a-5)+4(a-5) The given expression
2a2-10a+4a-20 The parentheses are removed by use of the distributive property
2a2-6a-20 Coefficients are added to enable combination of like terms
The above is simplified fully and no more computation is needed. The like terms were already grouped together and as such there was no need to rearrange the order.
2w-3+3(w-4)-5(w-6) The given expression. .
2w-3+3w-12-5w+30 Parentheses removed by distributive property.
2w+3w-5w-12+30 Commutative propertyof real numbers is .............
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