How To Multiply The Brackets | The Science

The Science

How to multiply the brackets

math in parentheses can contain variables and expressions of varying difficulty. For the multiplication of such expressions will have to find a solution in a general way, opening the brackets and simplifying the result. If the brackets are contained in the operations without variables, only the numerical values, it is not necessary to open the brackets, as if the computer user has access to his very considerable computing resources - it is easier to use them than to simplify the expression.

Instruction how to multiply out brackets

Step 1:

Multiplied consecutively each term (or decreases with deductible), contained in a bracket on the contents of all the other brackets, if you want to get a result in the general form. For example, suppose the original expression is written as follows: (5 + x)∗(X-6)∗(X + 2). Then the sequence of multiplication (ie disclosure brackets) gives the following result: (5 + x)∗(X-6)∗(X + 2) = (5∗6-5∗x)∗(5∗x + 5∗2) + (6∗x-x∗x)∗(x∗x + 2∗x) = (5∗6∗5∗x + 5∗6∗5∗2) - (5∗x∗5∗x + 5∗x∗5∗2) + (6∗x∗x∗x + 6∗x∗2∗x) - (x∗x∗x∗x + x∗x∗2∗x) = 5∗6∗5∗x + 5∗6∗5∗2 - 5∗x∗5∗x - 5∗x∗5∗2 + 6∗x∗x∗x + 6∗x∗2∗x - x∗x∗x∗x - x∗x∗2∗x = 150∗x + 300 - 25∗x² - 50∗x + 6∗X³ + 12∗x² - x∗X³ - 2∗X³.

Step 2:

Simplify obtained after expanding output, reducing the expression. For example, obtained in the previous step, the expression can be simplified as follows: 150∗x + 300 - 25∗x² - 50∗x + 6∗X³ + 12∗x² - x∗X³ - 2∗X³ = 100∗x + 300 - 13∗x² - 8∗x³ - x∗X³.

Step 3:

Use a calculator if you want to multiply the brackets contain only numeric values, no unknown variables. Built-in software calculator is in the operating system - if it is one of the versions of Windows, you can launch it from a link placed in the main menu in the section "Tools" under "Accessories" under "All Programs." The interface of this program is very simple and trouble evaluation of expressions in brackets and their subsequent multiplication, cause should not.

Step 4:

Use as an alternative to the standard calculator, calculators, built-in search engines. For example, suppose that you want to calculate the result of the expression given in the first step, with the proviso that X is equal to 4.75, that is (5 + 4.75)∗(6-4.75)∗(4.75 + 2). To calculate this value, go to the Google search site or Nigma and enter the expression in the query box in its original form (5 + 4.75) * (6-4.75) * (4.75 + 2). Google will answer 82.265625 immediately, without pressing the button, and Nigma needs to send data to the server by pressing the button.