A Difference of Squares
Part of the Exponents & Polynomials section of Coddy's Algebra journey. Lesson 52 of 64.
One more special product is a sum times a difference of the same two terms, such as (x+3)(x-3). The four products are x^2, -3x, 3x and -9. The two cross products are opposites, so they cancel.
What remains is x^2 - 9, a difference of squares. In letters, (a+b)(a-b) = a^2 - b^2. Because the cross products cancel, the product has no middle term.
You can use the difference of squares for mental arithmetic. To work out 21 times 19, write it as 21 * 19 = (20 + 1)(20 - 1) = 400 - 1 = 399. The two numbers are 20 plus 1 and 20 minus 1, so the product is 20 squared minus 1 squared.
Challenge
MediumExpand (x+6)(x-6) and collect the like 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