Basic Algebraic Identities and Expressions An algebraic identity is a statement that is always true, regardless of the values of its variables. It can be...
An algebraic identity is a statement that is always true, regardless of the values of its variables. It can be expressed with equal signs and is a mathematical statement that is equivalent to another statement.
An expression is a combination of numbers, variables, and operations that is evaluated to a single value. It is a specific value resulting from the evaluation of an algebraic expression.
Basic algebraic identities and expressions include:
Distributivity: a(b + c) = ab + ac
Combine like terms: a + b + c = (a + b) + c
Sum/difference of similar terms: (a + b) - (c + d) = (a - c) + (b - d)
Power of a sum: (a + b)^2 = a^2 + 2ab + b^2
Power of a difference: (a - b)^2 = a^2 - 2ab + b^2
Zero-product rule: a * 0 = 0
Examples:
Distributivity: 2(x + 3) = 2x + 6
Combine like terms: 3x + 2y - x + y = (3x - x) + (2y + y)
Sum of similar terms: 3^2 = 9, while 4^2 = 16
Power of a sum: (2 + 3)^2 = 4^2 = 16
Power of a difference: (5 - 3)^2 = 2^2 = 4
By understanding these basic algebraic identities and expressions, you can simplify and manipulate expressions, solve equations, and interpret mathematical results.