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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. 58 (page 499)

In the following exercises, add or subtract the polynomials.
$(m^{2} + 2 n^{2}) - (m^{2} - 8 m n - n^{2})$

Short Answer

Expert verified

Hence,

$(m^{2} + 2 n^{2}) 鈭� (m^{2} 鈭� 8 m n 鈭� n^{2}) = 3 n^{2} + 8 m n$

Step by step solution

01

Step 1. Given information

$\begin{array}{l} Thegivenexpressionsis \\ (m^{2} + 2 n^{2}) 鈭� (m^{2} 鈭� 8 m n 鈭� n^{2}) \\ Thesignbetweenpolynomialsis' 鈭�' . \end{array}$

02

Step 2. Subtract the polynomials

$\begin{array}{l} 鈬� (m^{2} + 2 n^{2}) 鈭� (m^{2} 鈭� 8 m n 鈭� n^{2}) \\ = m^{2} + 2 n^{2} 鈭� m^{2} + 8 m n + n^{2} [Rewritewithoutparentheses] \\ = m^{2} 鈭� m^{2} + 2 n^{2} + n^{2} + 8 m n [Combinetheliketerms] \\ = 0 + 3 n^{2} + 8 m n [Simplify] \\ = 3 n^{2} + 8 m n \end{array}$

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Most popular questions from this chapter

When you convert a number from decimal notation to scientific notation, how do you know if the exponent will be positive or negative

Determine whether each polynomial is a monomial, binomial, trinomial, or other polynomial. Then, find the degree of each polynomial

$(a) 64 k^{3} - 8 (b) 9 m^{3} + 4 m^{2} - 2 (c) \frac{5}{6} (d) 8 a^{4} - 7 a^{3} b - 6 a^{2} b^{2} - 4 a b^{3} + 7 b^{4} (e) - p^{4} q^{3}$

Use the Product Property for Exponents to explain $x 路 x = x^{2}$

Solve the square using the binomial squares pattern.

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

In the following exercises, find the product of $(x^{2} 鈥� + 鈥� 8 y) (8 x 鈥� 鈭� 鈥� y^{2})$ .

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