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Elementary Algebra

Lynn Marecek, MaryAnne Anthony-Smith

$Math Studyset 91影视 Explanations$ Math

2nd Edition 路 1240 pages

ISBN: 9780998625713

Chapter 6: Q. 67 (page 697)

In the following exercises, add or subtract the polynomials.
$(p^{3} - 3 p^{2} q) + (2 p q^{2} + 4 q^{3}) - (3 p^{2} q + p q^{2})$

Short Answer

Expert verified

The simplified form is $p^{3} - 6 p^{2} q + p q^{2} + 4 q^{3}$ .

Step by step solution

01

Step 1. Given information.

The given expression is:

$(p^{3} - 3 p^{2} q) + (2 p q^{2} + 4 q^{3}) - (3 p^{2} q + p q^{2})$

02

Step 2. Determine the value after simplification.

Simplify the given expression by combining the like terms.

$\begin{array}{rcl} (p^{3} - 3 p^{2} q) + (2 p q^{2} + 4 q^{3}) - (3 p^{2} q + p q^{2}) & = & p^{3} - 3 p^{2} q + 2 p q^{2} + 4 q^{3} - 3 p^{2} q - p q^{2} \\ = & p^{3} + (- 3 p^{2} q - 3 p^{2} q) + (2 p q^{2} - p q^{2}) + 4 q^{3} \\ = & p^{3} + (- 6 p^{2} q) + p q^{2} + 4 q^{3} \\ = & p^{3} - 6 p^{2} q + p q^{2} + 4 q^{3} \end{array}$

03

Step 3. Conclusion.

The simplified form is $p^{3} - 6 p^{2} q + p q^{2} + 4 q^{3}$ .

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