8 Pull It All Together

BIG idea Equivalence

You can represent algebraic expressions in many ways. When you add, subtract, multiply, divide, and factor polynomials, you replace one expression with an equivalent expression.

BIG idea Properties

The properties of real numbers are the basis of the laws of algebra. You can apply properties of real numbers, such as the Distributive Property, to polynomials.

Task 1

Solve. Show all of your work and explain your steps.

An archery target consists of a circular bull's-eye with radius x, surrounded by four rings with width y. What is the area of the outermost ring in terms of x and y?

Task 2

Solve. Show all of your work and explain your steps.

You are painting the outside of a jewelry box, including the bottom. To find the surface area (S.A.) of the jewelry box, you can use the formula S.A. = 2wℓ + 2ℓh + 2wh, where ℓ is the length, w is the width, and h is the height. What is the surface area of the jewelry box in terms of x?

Task 3

Solve. Show all of your work and explain your steps.

The volume of a square prism is 144 x 3 + 216 x 2 + 81 x . 144 x cubed . plus . 216 x squared . plus 81 x .  What is an expression that could describe the perimeter of one of the prism's square faces?

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