Advice 1: How to open brackets in the equation

Each student must learn to reveal the brackets in the equation. This procedure is important for the solution of mathematical, physical, and other tasks that require at least a minimum of computation.
How to open brackets in the equation
Instruction
1
So you have the equation. In some part of the equation is the expression in parentheses. To expand brackets, look at the sign before the parenthesis. If the sign is plus, when the expansion of brackets in an expression record, nothing will change: just remove the brackets. If there is a minus sign, after opening the brackets you need to change all the signs in the expression, standing initially in the parentheses to the opposite. For example, -(2x-3)=-2x+3.
2
The multiplication of two brackets.
If in the equation there is the product of two brackets, opening braces occur on the standard rule. Every member of the first brackets is multiplied by every member of the second bracket. The resulting numbers are added together. The product of two "pluses" or two "cons" gives the term a plus sign, and if the multipliers have different signs, the term gets a minus sign.
Let's consider an example.
(5x+1)(3x-4)=5x*3x-5x*4+1*3 1*4=15x^2-20x+3x-4=15x^2-17x-4.
3
Opening parentheses are also sometimes called construction of expression to a degree. The formula calculates the square and the cube must know by heart and remember.
(a+b)^2=a^2+2ab+b^2
(a-b)^2=a^2-2ab+b^2
(a+b)^3=a^3+3a^2*b+3ab^2+b^3
(a-b)^3=a^3-3a^2*b+3ab^2-b^3
Formula of construction of the expression in degree more than three can be obtained with the help of Pascal's triangle.

Advice 2: 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.
How to multiply brackets
Instruction
1
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.
2
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.
3
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.
4
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.
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