Chapter 5

\(\left(2 x^{2}+7 x+30\right) \div(x+2)\)

\(\left(-3 z^{4}\right)\left(-z^{2}\right)\)

\(\left(-z^{7}\right)^{3}\)

\(\left(3 x^{2}+20 x+4\right) \div(x+1)\)

\(\frac{\left(8 \times 10^{3} \mathrm{in} .\right)^{2}}{4 \times 10^{2} \mathrm{in} .}\)

\(\left(-x^{4}\right)^{2}\left(-x^{2}\right)^{3}\)

\(\left(3 x^{2}+19 x+5\right) \div(x+1)\)

\(\frac{\left(6 \times 10^{3} \mathrm{in} .\right)^{2}}{6 \times 10^{4} \mathrm{in} .}\)

\(\left(-z^{5}\right)^{2}\left(-z^{7}\right)^{3}\)

\(\left(6 \times 10^{-4} \mathrm{~m}\right)^{3}\)

\((3 x-7)(3 x+7)\)

\(\left(8 \times 10^{-5} \mathrm{~m}\right)^{3}\)

\(\left(c^{2}+8\right) \div(c+6)\)

\((a+b)(a+b)=a^{2}+2 a b+b^{2}\)

\(\left(6 \times 10^{4} \mathrm{~m}\right)^{3}\)

\((3 x)^{-2}\)

\(\left(w^{2}+9\right) \div(w+2)\)

\((a-b)(a-b)=a^{2}-2 a b+b^{2}\)

\(\left(8 \times 10^{5} \mathrm{~m}\right)^{3}\)

\((a+b)(a-b)=a^{2}-b^{2}\)

\(\frac{1}{4 \times 10^{8}}\)

\(\left(-\frac{3 x^{4}}{4 y^{9}}\right)\left(\frac{2 x^{7}}{9 y^{6}}\right)\)

\((a-b)(a+b)=a^{2}-b^{2}\)

\(-5 k^{2}(2 k-6)\)

. \(\frac{1}{5 \times 10^{6}}\)

. \(\left(-\frac{5 a^{3}}{6 b^{5}}\right)\left(\frac{2 a^{8}}{15 b^{4}}\right)\)

A customer borrows \(\$ 8500\) for 6 years at a simple interest rate of \(11.3 \%\). Find the simple interest.

Explain why "difference of squares" is a good name for the pattern \((a-b)(a+b)=a^{2}-b^{2}\).

\(5.2 \times 10^{-8} \mathrm{~g}+1.3 \times 10^{-8} \mathrm{~g}\)

\(\left(\frac{2 a^{3}}{7 b^{8}}\right)\left(\frac{21 b^{12}}{10 a}\right)\)

The pattern for the difference of squares is given as \((a-b)(a+b)=a^{2}-b^{2}\). Is this equivalent to the pattern \((a+b)(a-b)=a^{2}-b^{2} ?\) Explain.

\(3.9 \times 10^{-6} \mathrm{~m}+4.2 \times 10^{-6} \mathrm{~m}\)

\(\left(\frac{8 z^{5}}{15 w^{9}}\right)\left(\frac{3 w^{19}}{20 z}\right)\)

\(\left(x^{2}+5 x-24\right) \div(x+8)\)

The length of a rectangle is \(8 \mathrm{in}\). longer than the width. a. If \(W=\) width, write a polynomial expression in \(W\) that represents the length, and draw a diagram of the rectangle. Do not include the units. b. Write a polynomial expression in \(W\) that represents the perimeter. c. Write a polynomial expression in \(W\) that represents the area.

\(-\frac{3}{5} a\left(10 a+\frac{1}{2}\right)\)

\(5.2 \times 10^{-9} \mathrm{~g}+1.3 \times 10^{-8} \mathrm{~g}\)

\(\left(x^{2}+7 x-18\right) \div(x+9)\)

The width of a rectangle is \(10 \mathrm{~cm}\) shorter than the length. a. If \(L=\) length, write a polynomial expression in \(L\) that represents the width, and draw a diagram of the rectangle. Do not include the units. b. Write a polynomial expression in \(L\) that represents the perimeter. c. Write a polynomial expression in \(L\) that represents the area.

\(-\frac{5}{6} b\left(12 b+\frac{1}{4}\right)\)

\(3.9 \times 10^{-7} \mathrm{~m}+4.2 \times 10^{-6} \mathrm{~m}\)

\(\left(\frac{3 x^{4}}{5 z^{8}}\right)\left(\frac{5 z^{8}}{3 x^{4}}\right)\)

\(\left(x^{2}+27 x+180\right) \div(x+12)\)

\(8 k\left(2 k^{2}-k+5\right)\)

\(9.3 \times 10^{3} \mathrm{~kg}+4.8 \times 10^{3} \mathrm{~kg}\)

\(\left(40 x^{2}+122 x+55\right) \div(2 x+5)\)

The length of a rectangle is \(3 \mathrm{~cm}\) longer than twice the width. a. If \(W=\) width, write a polynomial expression in \(W\) that represents the length, and draw a diagram of the rectangle. Do not include the units. b. Write a polynomial expression in \(W\) that represents the perimeter. c. Write a polynomial expression in \(W\) that represents the area.

\(9 h\left(3 h^{2}-h+7\right)\)

\(7.9 \times 10^{4} \mathrm{~km}+6.8 \times 10^{4} \mathrm{~km}\)

Problem: Simplify: \(\left(24 x^{3}+8 x^{2}-2 x\right) \div(4 x)\) Incorrect Answer: \(\frac{24 x^{3}+8 x^{2}-2 x}{4 x}\) $$ \begin{aligned} &=\frac{6 \cdot 4 \cdot x \cdot x^{2}+2 \cdot 4 x^{2}-2 x}{4 \cdot x} \\ &=6 x^{2}+8 x^{2}-2 x \\ &=14 x^{2}-2 x \end{aligned} $$