Binomial Times Binomial
Part of the Exponents & Polynomials section of Coddy's Algebra journey. Lesson 49 of 64.
(x+2)(x+3) multiplies two packages. Treat the first as a single multiplier and distribute it, exactly as if it were a monomial: (x+2) * x + (x+2) * 3. Distribute each of those in turn, and every term of the first package has met every term of the second: x^2 + 3x + 2x + 6.
Collect the middle: x^2 + 5x + 6. Four little products, one collection. The pattern is worth naming: firsts, outers, inners, lasts; every pairing exactly once.
The middle terms are the news here. The x-terms 3x and 2x came from cross products, and their sum, 5, is the sum of the 2 and 3 you started with, while the constant 6 is their product. That observation becomes a factoring machine in the next section.
Challenge
MediumExpand (x+4)(x+2) and collect the middle terms.
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