Important Formulas: Algebraic Expressions | Mathematics (Maths) Class 7 (Old NCERT) PDF Download

Important Formulas

• Literal numbers are letters that stand for numbers.
• These literals and their combinations follow the rules of addition, subtraction, multiplication, and division, along with their properties.
• In x⁹, the number 9 is known as the index or exponent, while x is the base. In a⁵, 5 is the index and a is the base.
• A constant is a symbol with a fixed numerical value.
• A variable is a symbol that can take on different numerical values.
• An algebraic expression is formed by combining constants and variables using the fundamental operations of addition, subtraction, multiplication, and division.
• Expressions consist of terms, which are added together. For example, the terms 4xy and 7 combine to form the expression 4xy + 7.
• A term is a product of factors. In the expression 4xy + 7, the term 4xy consists of the factors 4, x, and y. Factors that include variables are called algebraic factors.
• The coefficient is the numerical part of a term. Any factor of a term can also be considered the coefficient of the remaining part.
• An expression with one or more terms is referred to as a polynomial. A one-term polynomial is a monomial, a two-term polynomial is a binomial, and a three-term polynomial is a trinomial.
• Terms with the same algebraic factors are called like terms, while those with different factors are called unlike terms. For instance, 4xy and -3xy are like terms, but 4xy and -3x are not.
• The sum or difference of like terms is another like term, where the coefficient is the sum or difference of those terms.
• When adding or subtracting algebraic expressions, we combine like terms to find their sum or difference.
• To subtract one expression from another, we change the sign of each term in the subtracted expression and then add the two expressions.
• When a grouping symbol preceded by a ' sign ' is removed or inserted, the sign of each term of the corresponding expression changes (from ' + ' to ‘− ' and from ‘− ' to + ').