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Intermediate Algebra

OPENSTAX

$Math Studyset Vaia Explanations$ Math

OER 2017 Edition · 1346 pages

ISBN: 9780998625720

Chapter 5: Q. 59 (page 499)

In the following exercises, add or subtract the polynomials.

Short Answer

Expert verified

Hence,

$(p^{3} - 3 p^{2} q) + (2 p q^{2} + 4 q^{3}) - (3 p^{2} q + p q^{2}) = 5 p^{3} - 6 p^{2} q + p q^{2}$

Step by step solution

01

Step 1. Given information

$\begin{array}{l} Thegivenexpressionsis \\ (p^{3} - 3 p^{2} q) + (2 p q^{2} + 4 q^{3}) - (3 p^{2} q + p q^{2}) \\ Wehavetoaddorsubtractthepolynomialsasapplicable. \end{array}$

02

Step 2. Simplify

$\begin{array}{l} \Rightarrow (p^{3} - 3 p^{2} q) + (2 p q^{2} + 4 q^{3}) - (3 p^{2} q + p q^{2}) \\ = p^{3} - 3 p^{2} q + 2 p q^{2} + 4 q^{3} - 3 p^{2} q - p q^{2} [Rewritewithoutparentheses] \\ = p^{3} + 4 q^{3} - 3 p^{2} q - 3 p^{2} q + 2 p q^{2} - p q^{2} [Combinetheliketerms] \\ = 5 p^{3} - 6 p^{2} q + p q^{2} [Simplify] \end{array}$

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Most popular questions from this chapter

Multiply each pair of conjugates using the product of the conjugates pattern.

$(p + \frac{4}{5} q) (p - \frac{4}{5} q)$

In the following exercises, multiply the binomials. Use any method.

$(6 p + 5) (p + 1)$

Multiply each pair of conjugates using the product of the conjugates pattern.

$(9 c + 5) (9 c - 5)$

In the following exercises, find the product of $(r^{6} + s^{6}) (r^{6} - s^{6})$ .

Solve the square using the binomial squares pattern.

${(4 y^{3} - 2)}^{2}$

See all solutions

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