Minding the Signs
Part of the Exponents & Polynomials section of Coddy's Algebra journey. Lesson 48 of 64.
When the multiplier is negative, its minus sign is part of every product. In -2x(x + 5), the multiplier is -2x, so each product is negative. -2x * x = -2x^2 and -2x * 5 = -10x. The answer is -2x^2 - 10x.
When there are negative terms inside as well, decide the sign of each product separately, using the rules for multiplying signed numbers. In -2x(x - 5), the first product is -2x^2. The second product is -2x times -5, which is 10x, because two negatives multiply to a positive. The result is -2x^2 + 10x.
Write the sign of each product as you distribute. A negative multiplier changes the sign of every term inside the parentheses. A positive term gives a negative product, and a negative term gives a positive product.
Challenge
MediumExpand -4x(x + 3). Decide the sign of each product 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