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Final: Area, Modeled

Part of the Exponents & Polynomials section of Coddy's Algebra journey. Lesson 62 of 64.

A square garden bed is x meters on each side. The design makes it a rectangle by adding 5 meters to one side and 2 meters to the other. The new sides are x + 5 and x + 2.

The area of a rectangle is its length times its width. Write the area as the product of the two sides, before you multiply anything out: a = (x+5)(x+2). The equation keeps both sides visible, so you can see where each number comes from.

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Challenge

Medium

A second bed is also x meters on each side to begin with. It is stretched by 6 meters on one side and 2 meters on the other. Write an equation for its area a as a product of the two sides. Do not expand the product.

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This lesson includes a short quiz. Start the lesson to answer it and track your progress.

quiz iconTest yourself

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