Like Terms, Only Stronger
Part of the Exponents & Polynomials section of Coddy's Algebra journey. Lesson 40 of 64.
With powers in play, like means: same letter, same exponent. x^2 and 2x^2 are like. 3x and x are like. x^2 and 3x are not: a square and a length are different kinds of thing, and no amount of adding turns one into the other.
Tidy x^2 + 3x + 2x^2 + x by gathering each kind: the squares, x^2 + 2x^2 = 3x^2; the plain x terms, 3x + x = 4x. Result: 3x^2 + 4x, a binomial in standard form, and no further collecting is possible.
A tidy polynomial has at most one term of each degree. That is what "simplified" means here, and it is the form every answer in the coming chapters wants to arrive at.
Challenge
MediumTidy x^2 + 5x + 4x^2 + x into standard form.
Try it yourself
Simplify the expression
Test yourselfThis lesson includes a short quiz. Start the lesson to answer it and track your progress.
All lessons in Exponents & Polynomials
1What a Power Is
Repeated MultiplicationSquares and CubesPowers of Negative NumbersWhere the Minus LivesRecap: First Powers4Power of a Power
A Power Raised AgainWhy Exponents MultiplyProduct Rule or Power Rule?The Rule in LettersRecap: Power of a Power2The Product Rule
Multiplying Same BasesWith CoefficientsMore Than Two FactorsThe Rule in LettersRecap: The Product Rule5Product and Quotient Powers
Every Factor Gets the PowerWith a Number InsideA Power of a QuotientAll Three Rules TogetherRecap: Products and Quotients8What a Polynomial Is
Terms with PowersThe DegreeLike Terms, Only StrongerRecap: Meet the Polynomials11Dividing by a Monomial
Splitting the FractionDividing by a Variable TermBigger SplitsCancel with CareRecap: Dividing3The Quotient Rule
Dividing Same BasesWhy Exponents SubtractWith CoefficientsThe Rule in LettersRecap: The Quotient Rule6Zero and Negative Exponents
The Zero ExponentZero at WorkNegative Means ReciprocalWriting Without NegativesPowers of TenRecap: Zero and Negative