How to multiply brackets

Bracketed mathematical operation can contain variables and expressions of various degrees of complexity. To multiply such expressions will have to look for a solution in a General view, opening the brackets and simplifying the result. If in the brackets of the operation variables, only numerical values, opening the parentheses is not necessary, as in the presence of a computer user has access to very significant computing resources – it is easier to use them than to simplify the expression.

Instruction

Peremeshayte consistently each summand (or minuend from the subtrahend) contained in one clause, the contents of all the other brackets if you want to obtain the result in General. For example, suppose the original expression is written as: (x+5)∗(6-x)∗(x+2). Then successive multiplication (that is, the disclosure of the brackets) will give the following result: (x+5)∗(6-x)∗(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.

Simplify obtained after disclosure of brackets is the result of reduced expression. For example, obtained in the previous step, the expression can be simplified thus: 150∗x + 300 - 25∗x2 - 50∗x + 6∗x3 + 12∗x2 - x∗x3 - 2∗x3 = 100∗x + 300 - 13∗x2 - 8∗x3 - x∗x3.

Use a calculator if you want to multiply brackets that contain numeric values only, no unknowns. Built-in software calculator is in an operating system - if this is one of the versions of Windows, then run it by using the links placed in the main menu to the section "business" subsection "Standard" under "All programs." The program's interface is very simple and hassle-free evaluating expressions in brackets and their subsequent multiplication, should not cause.

Use as an alternative to the standard calculator calculators, built-in search engine. For example, suppose you want to calculate the result of the expression given in the first step, assuming 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 website of the search engine Google or Nigma and enter the expression in the query in its original form (5+4.75)*(6-4.75)*(4.75+2). Google will reveal the answer 82.265625 immediately, without clicking, and Nigma needs to send data to the server by the push of a button.

Is the advice useful?