Simplifying Expressions

Pre-Algebra · Axiom Academy

LESSON Simplifying Expressions Like terms are the same "type" — so you can merge them by just adding their coefficients, while everything else stays put. Every term has a variable part — the letter (and power) attached to it. Two terms are like terms only when those variable parts match exactly ; the coefficient out front can be anything. Watch five terms sort themselves: the x 's drift to one bin, the y to another, and the bare number to its own. Same variable part, same bin. 3x and 5x · -2y and 7y · 4 and 9 (same variable part) 3x and 5y (different variables) · 2x and 3x^2 (different powers) 2. The Rule: Add the Coefficients Once two terms are like, combining them is mechanical: add the coefficients and keep the variable part unchanged . In the animation, 4x and -x slide together and fuse into one tile; the numbers 4 and -1 add to 3 , and the x rides along untouched. The lone +3 has no partner, so it just waits. Add the coefficients, keep the variable part The number multiplying the variable. In -x it is -1 (a bare variable has coefficient 1 ). The letter and its power. It is not changed by combining — x stays x . Simplify 4x + 3 - x . The like terms are 4x and -x ; the 3 is a lone constant. Add their coefficients: 4 + (-1) = 3 , so 4x - x = 3x .

This is the written version of the interactive lesson above. See the full Pre-Algebra course.