formulas or rules of abridged multiplication used in arithmetic, to be exact - in algebra, for faster calculation process large algebraic expressions.Themselves formula derived from the existing rules of algebra to multiply the number of polynomials.
Using these formulas provide fairly rapid solution of various mathematical problems, and also helps to implement the simplification of expressions.Rules allow you to perform algebraic manipulations, some manipulation of expressions, which can be accessed by following the left side of the expression on the right-hand side or the right side of convert (to get the expression in the left side of the equal sign).
Well-known formulas used to abbreviate multiplication on memory, as they are often used in solving problems and equations.The following are the basic formulas included in this list, and their name.
Square amount
To calculate the square of the sum necessary to find the sum of the square of the first term, the first term is twice the product of the second and the second square.As an expression of this rule is written as follows: (a + c) ² = a² + 2AS + s².
squared difference
To calculate the square of the difference, you need to calculate the sum of the square of the first number, twice the product of the first day of the second (taken with the opposite sign) and the square of the second number.As an expression of this rule is as follows: (a - c) ² = a² - + 2AS s².
difference squares
formula for the difference of two numbers, squared, is equal to the sum of these numbers on their difference.As an expression of the rule is as follows: a² - s² = (a + c) · (a - c).
Cube amount
To calculate the cube of the sum of two terms, it is necessary to calculate the sum of the cube of the first term, three times the product of the square of the first term and the second, three times the product of the first term and the second in the square and the cube of the second term.As an expression of this rule is as follows: (a + c) ³ = a³ 3a²s + + + s³ 3as².
sum of cubes
According to the formula, the sum of the cubes is equal to the product of the sum of these terms on their part-square difference.As an expression of this rule is as follows: a³ s³ + = (a + c) + (a² - ac + s²).
example. necessary to calculate the volume of the figure, which is formed by adding the two cubes.There are only the size of their parties.
If the values are small parties, then perform a calculation.
If the lengths of the sides are expressed in bulky numbers, in this case, simply apply the formula "Sum of cubes", which will greatly simplify the calculations.
Cube difference
cubic expression for the difference is: the sum of the first term of the third degree, three times the negative product of the square of the first term to the second, three times the product of the square of the first term and the second negative cube of the second term.In the form of a mathematical expression cube difference is as follows: (a - c) ³ = a³ - 3a²s + 3as² - s³.
difference cubes
Formula cubes difference different from the sum of the cubes is only one sign.Thus, the difference of cubes - a formula, equal to the difference between these numbers on the square of the sum of their part.In a mathematical expression difference cubes as follows: a3 - c3 = (a - c) (al + a2 + c2).
example. necessary to calculate the volume of a figure that remains after subtracting the amount of blue cube volume figures yellow, which is also a cube.It is known only to the value of the part of small and large cube.
If the values are small parties, the calculation is quite simple.And if the lengths of the sides are expressed in a large number, it is necessary to apply the formula, entitled "The difference cubes" (or "Cube difference") manager that will greatly simplify the calculations.
