Algebraic expressions are one or more terms containing variables and constants connected by mathematical operations. These can be monomials, binomials, trinomials and polynomials.
The process of reducing algebraic expressions involves multiplication and division, removing (expanding) brackets and collecting like terms. Collecting like terms is the most common way to simplify algebraic expressions.
Binomial expansion is the process of raising a binomial expression to a number of powers. The result is the binomial theorem, a mathematical theorem that applies to many different areas of mathematics.
When you expand a binomial, it is important to note patterns in the expanded powers. A pattern you should look for is that a + b starts with n, the power of the binomial, and decreases to 0.
The b + x terms start with 0 and increase to n. The x + y terms start with n and decrease to 0 and so on.
To find the values of the binomial coefficients, you can use Pascal’s triangle. This triangular array of numbers is named after French mathematician Blaise Pascal.
If you have a binomial with a high exponent, expanding it can be a lengthy process. The Binomial Theorem helps simplify the process of expanding it. This theorem also gives us a way to determine the middle term of a binomial.
Factorization is a fundamental algebraic procedure used to simplify expressions and solve equations. It consists of finding two numbers (both will be positive or negative) whose product is the last term and whose sum is the coefficient of the middle term.
The factoring of an expression can be done using a method based on common factors, the difference of squares, or a combination of these techniques. The latter is the most common method.
A univariate polynomial x of degree n with complex coefficients admits a unique factorization up to ordering and the signs of the factors. The unique factorization property is a version of the fundamental theorem of arithmetic and is an important aspect of computer algebra.
In addition, a number system containing division, such as real or complex numbers, also has a meaningful factorization, which can be achieved by writing an expression in lowest terms and separately factoring its numerator and denominator. However, it can be difficult to factor polynomials into linear factors with rational numbers.
Simplifying expressions is a key skill for GCSE students to master. Aspiring mathematicians are often asked to answer problems in the simplest terms possible, so knowing how to simplify an expression is critical for success.
Simplify an expression by removing parentheses, combining like terms, and adding the coefficients of the same variables. Applying the distributive property can help you do this.
Using the distributive property can also help you simplify fractions by multiplying each term within the parentheses to the number outside them. This is called a step-by-step procedure.
Simplifying fractions is essential for students to master. In order to do this, we need to cancel out common factors from both the numerator and denominator. This will give us the same simplest form of the fraction.
Rewriting is the process of remaking or devising something anew. It can be a literary work or a poem or even an article.
Several different modes of textual transformation can be identified under the rubric of rewriting including imitation, parody, burlesque, transposition, adaptation, pastiche and translation.
The term rewriting is a broader term than criticism and includes such practices as the appropriation of one text to express certain ideological or poetic interests. Moreover, it includes reading and rereading as well.
As a general rule, when you are working with formulas and equations, you need to do the same thing on both sides of the equation. This means you need to add, subtract, multiply or divide the same terms.