lesson
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Imagine a video game formula that calculates total player damage: 120+35x−4y2z. To program or balance this game, you have to know which parts scale, which parts stay fixed, and how every piece interacts.
Every algebraic expression is built from four fundamental building blocks: terms, factors, coefficients, and constants.
📊A clean visual diagram of an algebraic expression breakdown for '4x^2 - 7xy + 9'. Show the full expression at the top in large bold math font. Below it, draw colored callout brackets pointing to specific components: '+4' labeled as 'Coefficient', 'x^2' labeled as 'Variable Factor', the plus/minus signs showing how the whole string is split into 3 distinct 'Terms' (4x^2, -7xy, and +9), '-7' labeled as 'Coefficient', 'x' and 'y' labeled as 'Factors', and '+9' labeled as 'Constant Term'. Use a light neutral background (#f8f9fa), text color #1e2945, accent cards with soft borders (#e6e6e6), and clear color-coded pills (blue for coefficients, purple for variables, amber for constants). Fully responsive down to 350px.
How do you systematically take any expression apart without getting confused by minus signs or multiple variables?
Terms and Factors
A term is a single number, a single variable, or numbers and variables multiplied together. Terms are always separated from each other by addition (+) or subtraction (−) signs.
Inside each term, the individual pieces being multiplied together are called factors. In the term −5x2y, the factors are −5, x, x, and y.
📊An interactive-style visual demonstrating how an expression splits into terms and factors. Show the expression '8a^3b - 3c + 11' being sliced at the operators (+ and -) into 3 distinct term cards: Card 1 has '8a^3b' which unpacks downward into factors '8', 'a', 'a', 'a', 'b'; Card 2 has '-3c' unpacking into '-3' and 'c'; Card 3 has '11' (a single constant term). Clean pastel background boxes, crisp dark text (#1e2945), rounded corners, clear arrows showing the hierarchy from Expression -> Terms -> Factors.
Once you isolate a term, how do you distinguish the number driving it from a number that never changes?
Coefficients and Constants
A coefficient is the numerical factor multiplying the variable part of a term. For example, in −14xy3, the coefficient is −14.
A constant is a standalone number with no variable attached, meaning its value never changes regardless of the variable values.
When a term looks like it has no written number, such as x or −y2, remember that x=1⋅x and −y2=−1⋅y2. Their coefficients are 1 and −1 respectively.