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. [latex]\left(x+5\right)\left({x}^{2}+4x+3\right)[/latex]
2. [latex]\left(u+4\right)\left({u}^{2}+3u+2\right)[/latex]
3. [latex]\left(y+8\right)\left(4{y}^{2}+y-7\right)[/latex]
4. [latex]\left(a+10\right)\left(3{a}^{2}+a-5\right)[/latex]
5. [latex]\left(w-7\right)\left({w}^{2}-9w+10\right)[/latex]
6. [latex]\left(p-4\right)\left({p}^{2}-6p+9\right)[/latex]
7. [latex]\left(3q+1\right)\left({q}^{2}-4q-5\right)[/latex]
8. [latex]\left(6r+1\right)\left({r}^{2}-7r-9\right)[/latex]
9.[latex]\frac{51{m}^{4}+72{m}^{3}}{-3}[/latex]
10. [latex]\frac{310{y}^{4}-200{y}^{3}}{5{y}^{2}}[/latex]
11. [latex]\frac{412{z}^{8}-48{z}^{5}}{4{z}^{3}}[/latex]
12. [latex]\frac{46{x}^{3}+38{x}^{2}}{2{x}^{2}}[/latex]
13. [latex]\frac{51{y}^{4}+42{y}^{2}}{3{y}^{2}}[/latex]
14. [latex]\frac{24{p}^{2}-33p}{-3p}[/latex]
15. [latex]\frac{35{x}^{4}-21x}{-7x}[/latex]
16. [latex]\frac{63{m}^{4}-42{m}^{3}}{-7{m}^{2}}[/latex]
17. [latex]\frac{48{y}^{4}-24{y}^{3}}{-8{y}^{2}}[/latex]
18. [latex]\frac{63{a}^{2}{b}^{3}+72a{b}^{4}}{9ab}[/latex]
19. [latex]\frac{45{x}^{3}{y}^{4}+60x{y}^{2}}{5xy}[/latex]
Answers to Section 4.2 Odd Problems
1. [latex]{x}^{3}+9{x}^{2}+23x+15[/latex]
3. [latex]4{y}^{3}+33{y}^{2}+y−56[/latex]
5. [latex]{w}^{3}−16{w}^{2}+73w−70[/latex]
7. [latex]3{q}^{3}−11{q}^{2}−19q−5[/latex]
9. [latex]-17{m}^{4}−24{m}^{3}[/latex]
11. [latex]103{z}^{5}−12{z}^{2}[/latex]
13. [latex]17{y}^{2}+14[/latex]
15. [latex]-5{x}^{3}+3[/latex]
17. [latex]-6{y}^{2}+3y[/latex]
19. [latex]9{x}^{2}{y}^{3}+12y[/latex]
