Subtracting Polynomials
Part of the Exponents & Polynomials section of Coddy's Algebra journey. Lesson 43 of 64.
Subtraction is where the parentheses bite. 4x^2 + x - (x^2 - 3x) subtracts a whole polynomial, and the minus sign belongs to every term inside: subtracting a package means subtracting each thing in it.
Distribute the minus as you drop the parentheses, flipping each sign: - (x^2 - 3x) becomes - x^2 + 3x. Then collect as usual: 4x^2 - x^2 = 3x^2 and x + 3x = 4x, giving 3x^2 + 4x.
The double flip is the part to slow down for: subtracting -3x adds 3x. Fundamentals taught that two minus signs make a plus; here the rule earns its keep on every second term.
Challenge
MediumSubtract: 5x^2 + 2x - (2x^2 - 4x).
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