Like Terms, Only Stronger
Part of the Exponents & Polynomials section of Coddy's Algebra journey. Lesson 40 of 64.
Two terms are like terms when they have the same letter with the same exponent. The terms x^2 and 2x^2 are like terms. So are 3x and x. The terms x^2 and 3x are not like terms, because their exponents are different, and adding them cannot change that.
To simplify x^2 + 3x + 2x^2 + x, collect each kind of term separately. The x^2 terms give x^2 + 2x^2 = 3x^2. The x terms give 3x + x = 4x. The result, 3x^2 + 4x, is a binomial in standard form, and no more terms can be collected.
After you collect the like terms, a polynomial in x has at most one term of each degree. Write those terms from the largest exponent down to get standard form.
Challenge
MediumSimplify x^2 + 5x + 4x^2 + x and write the result in 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