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

Step 1. Given information.

The given expression is:

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

Step 2. Determine the value after simplification.

Simplify the given expression by combining the like terms.

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

Step 3. Conclusion.

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

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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

Step by step solution

Step 1. Given information.

Step 2. Determine the value after simplification.

Step 3. Conclusion.

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In the following exercises, add or subtract the polynomials.(p3-3p2q)+(2pq2+4q3)-(3p2q+pq2)

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Determine the value after simplification.

Step 3. Conclusion.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Mechanics Maths

Applied Mathematics

Geometry

Calculus

Logic and Functions

Theoretical and Mathematical Physics

Study anywhere. Anytime. Across all devices.

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