Algebraic expressions and identities: What are expressions?
Algebra is a branch of Mathematics that deals with the use of letters to represent numbers (unknown quantities). Algebra allows us to write rules and formulas using variables, constants, etc., which is a powerful method for determining unknowns. Algebra is very useful in solving puzzles and logical reasoning questions, mathematical puzzles, and tricky puzzles in everyday life. Since letters represent unknown numbers, we can also perform mathematical operations on these letters, which leads to the study of Algebraic Expressions and Identification.
Examples of algebraic expressions: x + 3, 4xy + 7, 2y – 5, etc.
Algebraic expressions are formed using variables (letters) and constants. In the expression 4xy + 7, x and y are variables while 7 is a constant. The value of the expression changes according to the values chosen for the variables contained within it. Therefore, as y takes different values, the value of 2y – 5 continues to change. When y = 2, 2y – 5 = 2(2) – 5 = –1; when y = 0, 2y – 5 = 2 × 0 –5 = –5, etc
Terminology, coefficients and coefficients
Take the term 2y -5. This expression is made up of two terms, 2y and 5. The terms are added to form the expression. The terms themselves can be formed as products of factors. The term 2y is the product of 2 and y. The term 5 is made up of only one factor, i.e. 5.
Another example, 3xy – 4x has two terms 3xy and 4x. The term 3xy is the product of the factors 3, x and y. The coefficient of a term is called the numerical coefficient or simply the coefficient. The coefficient in the 3xy term is 3 and the coefficient in the 4x term is 4.
Monomial, binomial and polynomial
Monomial: Expressions containing only one term are called Monomials.
Binomial: Expression containing two terms is called Binomial.
Trinomial: An expression containing three terms is called a Trinomial.
Polynomials: Expressions containing one or more terms with non-zero coefficients (with variables having non-negative exponents) are called Polynomials. A polynomial can contain any term, one or more than one.
Algebraic expressions and identity: What is identity?
We will look at three useful congruences for learning Algebraic Expressions. These identities are obtained by multiplying one binomial by another binomial.
Categories: Optical Illusion
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