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Intermediate Algebra

OPENSTAX

$Math Studyset 91影视 Explanations$ Math

OER 2017 Edition 路 1346 pages

ISBN: 9780998625720

Chapter 5: Q. 5.10 (page 491)

$Find the :difference (9 b^{2} - 5 b - 4) - (3 b^{2} - 5 b - 7)$

Short Answer

Expert verified

The difference of the given polynomials is $6 b^{2} + 3$

Step by step solution

01

Step 1. Given information

$\begin{array}{l} Thegivenpolynomialexpressionis \\ (9 b^{2} 鈭� 5 b 鈭� 4) 鈭� (3 b^{2} 鈭� 5 b 鈭� 7) \\ Wehavetofindthedifference. \end{array}$

02

Step 2. Distribute and identify like terms

$\begin{array}{l} Wehave (9 b^{2} 鈭� 5 b 鈭� 4) 鈭� (3 b^{2} 鈭� 5 b 鈭� 7) \\ Distributeandidentifyliketermsandthenrearrangetheterms \\ 鈬� (9 b^{2} 鈭� 5 b 鈭� 4) 鈭� (3 b^{2} 鈭� 5 b 鈭� 7) = \underset{炉}{9 b^{2}} 鈭� \underset{炉}{\underset{炉}{3 b}} 鈭� 4 鈭� \underset{炉}{3 b^{2}} + \underset{炉}{\underset{炉}{5 b}} + 7 \\ = (9 鈭� 3) y^{2} + (鈭� 5 + 5) b 鈭� 4 + 7 \\ \begin{array}{l} = 6 b^{2} + 0 b + 3 \\ = 6 b^{2} + 3 \end{array} \end{array}$

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Most popular questions from this chapter

Determine whether each polynomial is a monomial, binomial, trinomial, or other polynomial. Then, find the degree of each polynomial $(a) - 5 (b) 8 y^{3} - 7 y^{2} - y - 3 (c) - 3 x^{2} y - 5 x y + 9 x y^{3} (d) 81 m^{2} - 4 n^{2} (e) - 3 x^{6} y^{3} z$

Simplify ${(\frac{1}{3} m^{3} n^{2})}^{4} {(9 m^{8} n^{3})}^{2}$

Explain why $- 5^{3} = (- 5)^{3}$ but $- 5^{4} 鈮� (- 5)^{4}$

$Add: (a) 3 m^{2} + n^{2} - 7 m^{2} (b) p q^{2} - 6 p - 5 q^{2} .$

Solve the square using the binomial squares pattern.

${(\frac{1}{5} x - \frac{1}{7} y)}^{2}$

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