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Final: The Big Tidy

Part of the Exponents & Polynomials section of Coddy's Algebra journey. Lesson 61 of 64.

To simplify a sum of two products, expand each product on its own first. Each product of two binomials gives four terms. Then collect the like terms from both expansions together.

For (x+1)(x+2) + (x+3)(x+4): the first product expands to x^2 + 3x + 2, and the second expands to x^2 + 7x + 12. Adding them and collecting like terms gives 2x^2 + 10x + 14.

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Challenge

Hard

Simplify (x+1)(x+3) + (x+4)(x+5). Expand both products, then collect the like terms.

Try it yourself

(x+1)(x+3) + (x+4)(x+5)

Simplify the expression

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This 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 Powers

4Power of a Power

A Power Raised AgainWhy Exponents MultiplyProduct Rule or Power Rule?The Rule in LettersRecap: Power of a Power

7Scientific Notation

Very Large NumbersBack to Standard FormMore Practice, Bigger NumbersVery Small NumbersMultiplying the NotationRecap: Scientific Notation

10Multiplying Polynomials

Monomial Times PolynomialMinding the SignsBinomial Times BinomialWith CoefficientsThe Square of a BinomialA Difference of SquaresRecap: Multiplying

2The Product Rule

Multiplying Same BasesWith CoefficientsMore Than Two FactorsThe Rule in LettersRecap: The Product Rule

5Product and Quotient Powers

Every Factor Gets the PowerWith a Number InsideA Power of a QuotientAll Three Rules TogetherRecap: Products and Quotients

8What a Polynomial Is

Terms with PowersThe DegreeLike Terms, Only StrongerRecap: Meet the Polynomials

11Dividing by a Monomial

Splitting the FractionDividing by a Variable TermBigger SplitsCancel with CareRecap: Dividing

3The Quotient Rule

Dividing Same BasesWhy Exponents SubtractWith CoefficientsThe Rule in LettersRecap: The Quotient Rule

6Zero and Negative Exponents

The Zero ExponentZero at WorkNegative Means ReciprocalWriting Without NegativesPowers of TenRecap: Zero and Negative

9Adding and Subtracting

Adding PolynomialsSubtracting PolynomialsThe Minus Reaches EverythingPerimeter as a PolynomialRecap: Add and Subtract

12Final Challenges

Final: Three Rules, One LineFinal: Scientific NotationFinal: The Big TidyFinal: Area, ModeledFinal: Area, ExpandedFinal: Divide and Conquer