The Square of a Binomial
Part of the Exponents & Polynomials section of Coddy's Algebra journey. Lesson 51 of 64.
(x+3)^2 is the square of a binomial. The exponent does not distribute over the plus sign, so the answer is not x^2 + 9. A power of a binomial means the binomial multiplied by itself: (x+3)(x+3).
Write the four products: x^2, 3x, 3x and 9. The two cross products are equal, and they are the terms that x^2 + 9 leaves out. Collecting gives x^2 + 6x + 9.
The square of a binomial is (a + b)^2 = a^2 + 2ab + b^2. The middle term is the sum of the two equal cross products. Check with numbers: (3 + 4)^2 = 49, but 3^2 + 4^2 = 25. The difference is 2 * 3 * 4 = 24, which is the middle term that the second calculation leaves out.
Challenge
MediumExpand (x+4)^2. Do not leave out the middle term.
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