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FOIL Rule
In secondary school, ''FOIL'' is a mnemonic for the standard method of multiplying two binomials—hence the method may be referred to as the FOIL method. The word ''FOIL'' is an acronym for the four terms of the product: * First ("first" terms of each binomial are multiplied together) * Outer ("outside" terms are multiplied—that is, the first term of the first binomial and the second term of the second) * Inner ("inside" terms are multiplied—second term of the first binomial and first term of the second) * Last ("last" terms of each binomial are multiplied) The general form is : (a + b)(c + d) = \underbrace_\text + \underbrace_\text + \underbrace_\text + \underbrace_\text. Note that is both a "first" term and an "outer" term; is both a "last" and "inner" term, and so forth. The order of the four terms in the sum is not important and need not match the order of the letters in the word FOIL. History The FOIL method is a special case of a more general method for multip ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Addition
Addition (usually signified by the Plus and minus signs#Plus sign, plus symbol ) is one of the four basic Operation (mathematics), operations of arithmetic, the other three being subtraction, multiplication and Division (mathematics), division. The addition of two Natural number, whole numbers results in the total amount or ''summation, sum'' of those values combined. The example in the adjacent image shows a combination of three apples and two apples, making a total of five apples. This observation is equivalent to the Expression (mathematics), mathematical expression (that is, "3 ''plus'' 2 is Equality (mathematics), equal to 5"). Besides counting items, addition can also be defined and executed without referring to concrete objects, using abstractions called numbers instead, such as integers, real numbers and complex numbers. Addition belongs to arithmetic, a branch of mathematics. In algebra, another area of mathematics, addition can also be performed on abstract objects su ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mnemonic Acronyms
A mnemonic ( ) device, or memory device, is any learning technique that aids information retention or retrieval (remembering) in the human memory for better understanding. Mnemonics make use of elaborative encoding, retrieval cues, and imagery as specific tools to encode information in a way that allows for efficient storage and retrieval. Mnemonics aid original information in becoming associated with something more accessible or meaningful—which, in turn, provides better retention of the information. Commonly encountered mnemonics are often used for lists and in auditory form, such as short poems, acronyms, initialisms, or memorable phrases, but mnemonics can also be used for other types of information and in visual or kinesthetic forms. Their use is based on the observation that the human mind more easily remembers spatial, personal, surprising, physical, sexual, humorous, or otherwise "relatable" information, rather than more abstract or impersonal forms of information. ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Elementary Algebra
Elementary algebra encompasses the basic concepts of algebra. It is often contrasted with arithmetic: arithmetic deals with specified numbers, whilst algebra introduces variables (quantities without fixed values). This use of variables entails use of algebraic notation and an understanding of the general rules of the operations introduced in arithmetic. Unlike abstract algebra, elementary algebra is not concerned with algebraic structures outside the realm of real and complex numbers. It is typically taught to secondary school students and builds on their understanding of arithmetic. The use of variables to denote quantities allows general relationships between quantities to be formally and concisely expressed, and thus enables solving a broader scope of problems. Many quantitative relationships in science and mathematics are expressed as algebraic equations. Algebraic notation Algebraic notation describes the rules and conventions for writing mathematical expressio ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Binomial Theorem
In elementary algebra, the binomial theorem (or binomial expansion) describes the algebraic expansion of powers of a binomial. According to the theorem, it is possible to expand the polynomial into a sum involving terms of the form , where the exponents and are nonnegative integers with , and the coefficient of each term is a specific positive integer depending on and . For example, for , (x+y)^4 = x^4 + 4 x^3y + 6 x^2 y^2 + 4 x y^3 + y^4. The coefficient in the term of is known as the binomial coefficient \tbinom or \tbinom (the two have the same value). These coefficients for varying and can be arranged to form Pascal's triangle. These numbers also occur in combinatorics, where \tbinom gives the number of different combinations of elements that can be chosen from an -element set. Therefore \tbinom is often pronounced as " choose ". History Special cases of the binomial theorem were known since at least the 4th century BC when Greek mathematician Euclid ment ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Associativity
In mathematics, the associative property is a property of some binary operations, which means that rearranging the parentheses in an expression will not change the result. In propositional logic, associativity is a valid rule of replacement for expressions in logical proofs. Within an expression containing two or more occurrences in a row of the same associative operator, the order in which the operations are performed does not matter as long as the sequence of the operands is not changed. That is (after rewriting the expression with parentheses and in infix notation if necessary), rearranging the parentheses in such an expression will not change its value. Consider the following equations: \begin (2 + 3) + 4 &= 2 + (3 + 4) = 9 \,\\ 2 \times (3 \times 4) &= (2 \times 3) \times 4 = 24 . \end Even though the parentheses were rearranged on each line, the values of the expressions were not altered. Since this holds true when performing addition and multiplication on any real ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Antidiagonal
In linear algebra, the main diagonal (sometimes principal diagonal, primary diagonal, leading diagonal, major diagonal, or good diagonal) of a matrix A is the list of entries a_ where i = j. All off-diagonal elements are zero in a diagonal matrix. The following four matrices have their main diagonals indicated by red ones: :\begin \color & 0 & 0\\ 0 & \color & 0\\ 0 & 0 & \color\end \qquad \begin \color & 0 & 0 & 0 \\ 0 & \color & 0 & 0 \\ 0 & 0 & \color & 0 \end \qquad \begin \color & 0 & 0 \\ 0 & \color & 0 \\ 0 & 0 & \color \\ 0 & 0 & 0 \end \qquad \begin \color & 0 & 0 & 0 \\ 0 & \color & 0 & 0 \\ 0 & 0 &\color & 0 \\ 0 & 0 & 0 & \color \end \qquad Antidiagonal The antidiagonal (sometimes counter diagonal, secondary diagonal, trailing diagonal, minor diagonal, off diagonal, or bad diagonal) of an order N square matrix B is the collection of entries b_ such that i + j = N+1 for all 1 \leq i, j \leq N. That is, it runs from the top right corner to the bottom left corner. ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Factorization
In mathematics, factorization (or factorisation, see American and British English spelling differences#-ise, -ize (-isation, -ization), English spelling differences) or factoring consists of writing a number or another mathematical object as a product of several ''factors'', usually smaller or simpler objects of the same kind. For example, is a factorization of the integer , and is a factorization of the polynomial . Factorization is not usually considered meaningful within number systems possessing division ring, division, such as the real number, real or complex numbers, since any x can be trivially written as (xy)\times(1/y) whenever y is not zero. However, a meaningful factorization for a rational number or a rational function can be obtained by writing it in lowest terms and separately factoring its numerator and denominator. Factorization was first considered by Greek mathematics, ancient Greek mathematicians in the case of integers. They proved the fundamental theorem o ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Factorization
In mathematics, factorization (or factorisation, see American and British English spelling differences#-ise, -ize (-isation, -ization), English spelling differences) or factoring consists of writing a number or another mathematical object as a product of several ''factors'', usually smaller or simpler objects of the same kind. For example, is a factorization of the integer , and is a factorization of the polynomial . Factorization is not usually considered meaningful within number systems possessing division ring, division, such as the real number, real or complex numbers, since any x can be trivially written as (xy)\times(1/y) whenever y is not zero. However, a meaningful factorization for a rational number or a rational function can be obtained by writing it in lowest terms and separately factoring its numerator and denominator. Factorization was first considered by Greek mathematics, ancient Greek mathematicians in the case of integers. They proved the fundamental theorem o ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Monomial
In mathematics, a monomial is, roughly speaking, a polynomial which has only one term. Two definitions of a monomial may be encountered: # A monomial, also called power product, is a product of powers of variables with nonnegative integer exponents, or, in other words, a product of variables, possibly with repetitions. For example, x^2yz^3=xxyzzz is a monomial. The constant 1 is a monomial, being equal to the empty product and to x^0 for any variable x. If only a single variable x is considered, this means that a monomial is either 1 or a power x^n of x, with n a positive integer. If several variables are considered, say, x, y, z, then each can be given an exponent, so that any monomial is of the form x^a y^b z^c with a,b,c non-negative integers (taking note that any exponent 0 makes the corresponding factor equal to 1). # A monomial is a monomial in the first sense multiplied by a nonzero constant, called the coefficient of the monomial. A monomial in the first sense is a special c ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Like Terms
In mathematics, like terms are summands in a sum that differ only by a numerical factor. Like terms can be regrouped by adding their coefficients. Typically, in a polynomial expression, like terms are those that contain the same variables to the same powers, possibly with different coefficients. More generally, when some variable are considered as parameters, like terms are defined similarly, but "numerical factors" must be replaced by "factors depending only on the parameters". For exemple, when considering a quadratic equation, one considers often the expression :(x-r)(x-s), where r and s are the roots A root is the part of a plant, generally underground, that anchors the plant body, and absorbs and stores water and nutrients. Root or roots may also refer to: Art, entertainment, and media * ''The Root'' (magazine), an online magazine focusing ... of the equation and may be considered as parameters. Then, expanding the above product and regrouping the like terms gives : ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Multiplication
Multiplication (often denoted by the cross symbol , by the mid-line dot operator , by juxtaposition, or, on computers, by an asterisk ) is one of the four elementary mathematical operations of arithmetic, with the other ones being addition, subtraction, and division. The result of a multiplication operation is called a ''product''. The multiplication of whole numbers may be thought of as repeated addition; that is, the multiplication of two numbers is equivalent to adding as many copies of one of them, the ''multiplicand'', as the quantity of the other one, the ''multiplier''. Both numbers can be referred to as ''factors''. :a\times b = \underbrace_ For example, 4 multiplied by 3, often written as 3 \times 4 and spoken as "3 times 4", can be calculated by adding 3 copies of 4 together: :3 \times 4 = 4 + 4 + 4 = 12 Here, 3 (the ''multiplier'') and 4 (the ''multiplicand'') are the ''factors'', and 12 is the ''product''. One of the main properties of multiplication is ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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