Algebra I: An Introduction

Algebra uses letters, called variables, to represent unknown numbers. A constant is a fixed numerical value. A term is a number, a variable, or a product of numbers and variables (e.g., 3x, 7, -2y²). The numerical part of a term that multiplies the variable(s) is called the coefficient (e.g., in 3x, 3 is the coefficient). An algebraic expression is a combination of terms connected by addition or subtraction (e.g., 3x + 7, 2a - 5b + 1). Like terms are terms that have the exact same variable part (e.g., 3x and -5x, 2y² and 7y²).

To evaluate an algebraic expression, you replace each variable with its given numerical value and then calculate the result using the correct order of operations (BODMAS/PEMDAS).

You can only add or subtract like terms. To do this, you add or subtract their coefficients and keep the variable part exactly the same. Unlike terms cannot be combined through addition or subtraction.

To multiply algebraic terms, first multiply their numerical coefficients. Then, multiply their variable parts. If the same variable is multiplied, you add their powers (e.g., x × x = x², x² × x³ = x⁵).

To multiply a term by an expression inside brackets, you use the distributive law. This means you multiply the term outside the bracket by each term inside the bracket separately.

To multiply two expressions (e.g., two binomials), you must multiply each term in the first expression by each term in the second expression. This is an application of the distributive law. For two binomials (a+b)(c+d), a common mnemonic is FOIL (First, Outer, Inner, Last) to ensure all pairs are multiplied.