Section 4.2:  Algebraic Transformations of Expressions

Amy Graham Goodman

Section 4.2: Algebraic Transformations of Expressions

Learning Objectives

In this section, you will:

Determine a strategy for transforming an algebraic expression into sums/differences of power functions.
Execute a strategy for transforming an algebraic expression into sums/differences of power functions.

Let’s Get Started…

Check out Khan Academy’s Reverse Power Rule: Rewriting Before Integrating

Reload for a fresh batch of problems
Answers are automatically checked!

https://www.khanacademy.org/math/ap-calculus-ab/ab-integration-new/ab-6-8a/e/reverse-power-rule-rewriting

Section 4.2 Exercises

This content comes directly from OpenStax’s textbook Elementary Algebra Section 6.3 Multiply Polynomials and Section 6.6 Divide Polynomials.

Access these resources for free at https://openstax.org/books/elementary-algebra-2e/pages/6-3-multiply-polynomials and https://openstax.org/books/elementary-algebra-2e/pages/6-6-divide-polynomials

[Answers to odd problem numbers are provided at the end of the problem set. Just scroll down!]

Rewrite each expression below as sums/differences of power functions and (potentially) constants.

1. $(x + 5) (x^{2} + 4 x + 3)$

2. $(u + 4) (u^{2} + 3 u + 2)$

3. $(y + 8) (4 y^{2} + y - 7)$

4. $(a + 10) (3 a^{2} + a - 5)$

5. $(w - 7) (w^{2} - 9 w + 10)$

6. $(p - 4) (p^{2} - 6 p + 9)$

7. $(3 q + 1) (q^{2} - 4 q - 5)$

8. $(6 r + 1) (r^{2} - 7 r - 9)$

9. $\frac{51 m^{4} + 72 m^{3}}{- 3}$

10. $\frac{310 y^{4} - 200 y^{3}}{5 y^{2}}$

11. $\frac{412 z^{8} - 48 z^{5}}{4 z^{3}}$

12. $\frac{46 x^{3} + 38 x^{2}}{2 x^{2}}$

13. $\frac{51 y^{4} + 42 y^{2}}{3 y^{2}}$

14. $\frac{24 p^{2} - 33 p}{- 3 p}$

15. $\frac{35 x^{4} - 21 x}{- 7 x}$

16. $\frac{63 m^{4} - 42 m^{3}}{- 7 m^{2}}$

17. $\frac{48 y^{4} - 24 y^{3}}{- 8 y^{2}}$

18. $\frac{63 a^{2} b^{3} + 72 a b^{4}}{9 a b}$

19. $\frac{45 x^{3} y^{4} + 60 x y^{2}}{5 x y}$

Answers to Section 4.2 Odd Problems

1. $x^{3} + 9 x^{2} + 23 x + 15$

3. $4 y^{3} + 33 y^{2} + y - 56$

5. $w^{3} - 16 w^{2} + 73 w - 70$

7. $3 q^{3} - 11 q^{2} - 19 q - 5$

9. $- 17 m^{4} - 24 m^{3}$

11. $103 z^{5} - 12 z^{2}$

13. $17 y^{2} + 14$

15. $- 5 x^{3} + 3$

17. $- 6 y^{2} + 3 y$

19. $9 x^{2} y^{3} + 12 y$

License

Icon for the Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License

Baylor University's Co-requisite Supplement for Calculus I Copyright © 2023 by Amy Graham Goodman is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License, except where otherwise noted.