Add, subtract, and multiply linear expressions

Learning Objectives Identify and define key components of linear expressions, such as terms, coefficients, and constants. Correctly combine like terms within a linear expression. Add two or more linear expressions by combining their like terms. Subtract one linear expression from another, correctly handling the distribution of the negative sign. Multiply a linear expression by a constant using the distributive property. Simplify linear expressions involving a combination of addition, subtraction, and multiplication by a constant. Ever wonder how mathematicians simplify complex instructions into neat, manageable steps? 🤔 Just like organizing your backpack, simplifying expressions helps us make sense of math problems! In this lesson, you'll learn to combine, separate, a...

TermDefinitionExample ExpressionA mathematical phrase that can contain numbers, variables, and operation symbols (like +, -, ×, ÷), but does not contain an equality sign (=).$3x + 5$ Linear ExpressionAn algebraic expression where the highest power of any variable is 1. It does not contain variables multiplied together or variables in the denominator.$2y - 7$ TermThe parts of an expression that are separated by addition or subtraction signs.In $4x + 2y - 9$, the terms are $4x$, $2y$, and $-9$. Like TermsTerms that have the exact same variable(s) raised to the exact same power(s). Only the coefficients can be different.$5x$ and $-2x$ are like terms; $3y$ and $7y$ are like terms. CoefficientThe numerical factor that multiplies a variable in a term.In $6m$, the coefficient is $6$. In $-y$, th...

Combining Like Terms (Addition/Subtraction) $ax + bx = (a+b)x$ and $ax - bx = (a-b)x$ To add or subtract like terms, keep the variable part the same and add or subtract their coefficients. Distributive Property (Multiplication) $a(b+c) = ab + ac$ and $a(b-c) = ab - ac$ To multiply a number by an expression in parentheses, multiply the number by each term inside the parentheses. Subtracting Linear Expressions $(ax+b) - (cx+d) = ax+b - cx - d$ When subtracting an expression, distribute the negative sign to EVERY term inside the second set of parentheses, changing the sign of each term, then combine like terms.