Minding the Signs
Part of the Exponents & Polynomials section of Coddy's Algebra journey. Lesson 48 of 64.
A negative multiplier distributes its minus along with everything else. -2x(x + 5): the factor is -2x, so each product inherits the sign. -2x * x = -2x^2, and -2x * 5 = -10x: the answer is -2x^2 - 10x.
When the inside holds negatives too, the sign rules from chapter one of Fundamentals decide each product separately: -2x(x - 5) gives -2x^2 + 10x, the second product flipping to plus because two negatives multiply to a positive.
The safe habit: write each product with its sign before moving to the next term. Sign slips in distribution are the single most common error in this whole topic, and they are all avoidable at this one moment.
Challenge
MediumExpand -4x(x + 3), deciding each sign as you go.
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 Power7Scientific Notation
Very Large NumbersBack to Standard FormMore Practice, Bigger NumbersVery Small NumbersMultiplying the NotationRecap: Scientific Notation10Multiplying Polynomials
Monomial Times PolynomialMinding the SignsBinomial Times BinomialWith CoefficientsThe Square of a BinomialA Difference of SquaresRecap: Multiplying2The 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