The Minus Reaches Everything
Part of the Exponents & Polynomials section of Coddy's Algebra journey. Lesson 44 of 64.
Longer package, same law. 2x^2 - (x^2 - 4x + 1) subtracts a trinomial, and all three terms flip on the way out: 2x^2 - x^2 + 4x - 1.
The most commonly dropped flip is the last one, the lonely constant at the end of the package. Count the terms inside before you start, flip exactly that many signs, and the error has nowhere to hide.
Collect what remains: 2x^2 - x^2 = x^2, and the rest stands alone: x^2 + 4x - 1.
Challenge
MediumSimplify 3x^2 - (2x^2 - 5x + 2).
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 Negative9Adding and Subtracting
Adding PolynomialsSubtracting PolynomialsThe Minus Reaches EverythingPerimeter as a PolynomialRecap: Add and Subtract