Binomial Times Binomial
Part of the Exponents & Polynomials section of Coddy's Algebra journey. Lesson 49 of 64.
To multiply two binomials, such as (x+2)(x+3), treat the first binomial as a single multiplier and distribute it over the second: (x+2) * x + (x+2) * 3. Then distribute each of those products in turn. Now every term of the first binomial has been multiplied by every term of the second: x^2 + 3x + 2x + 6.
Collect the middle terms to get x^2 + 5x + 6. There are four products in all: the first terms, the outer terms, the inner terms and the last terms. Each pair of terms is multiplied once.
The two middle terms, 3x and 2x, are the cross products. They add to 5x. Their coefficient, 5, is the sum of 2 and 3, and the constant 6 is the product of 2 and 3. You will use this relationship to factor trinomials 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