Expansion of Binomials| Algebra| ENGG10 LE1 Problem 8

# Itemized Textbook Solutions

Expand the following binomial: (x-1/x)^5.

Perform the given operations of the following polynomial

Perform the given operations of the following polynomial

Perform the given operations of the following polynomial

Simplify the given expression. Write the answer with positive exponents.

Simplify the given expression. Write the answer with positive exponents.

Simplify the given expression. Write the answer with positive exponents. $latex \left(\frac{3^2}{a^3}\right)^{-2}\cdot \left(\frac{a^4}{2^2}\right)^2&s=2&bg=ffffff&fg=000000$ SOLUTION: $latex \left(\frac{3^2}{a^3}\right)^{-2}\cdot \:\left(\frac{a^4}{2^2}\right)^2=\frac{\left(3^2\right)^{-2}}{\left(a^3\right)^{-2}}\cdot \frac{\left(a^4\right)^2}{\left(2^2\right)^2}&s=1&bg=ffffff&fg=000000$ $latex =\frac{3^{-4}}{a^{-6}}\cdot \frac{a^8}{2^4}&s=1&bg=ffffff&fg=000000$ $latex =\frac{\frac{1}{3^4}}{\frac{1}{a^6}}\cdot \frac{a^8}{2^4}&s=1&bg=ffffff&fg=000000$ $latex =\frac{a^6}{3^4}\cdot \frac{a^8}{2^4}&s=1&bg=ffffff&fg=000000$ $latex =\frac{a^6}{81}\cdot \frac{a^8}{16}&s=1&bg=ffffff&fg=000000$ $latex =\frac{a^{6+8}}{1296}&s=1&bg=ffffff&fg=000000$ $latex =\frac{a^{14}}{1296}&s=1&bg=ffffff&fg=000000$

A farmer wants to fence off his four-sided plot of flat land. He measures the first three sides, shown as A, B, and C in the figure, and then correctly calculates the length and orientation of the fourth side D. What is his result?

You fly 32.0 km in a straight line in still air in the direction 35.0° south of west. (a) Find the distances you would have to fly straight south and then straight west to arrive at the same point. (This determination is equivalent to finding the components of the displacement along the south and west directions.) (b) Find the distances you would have to fly first in a direction 45.0º south of west and then in a direction 45.0° west of north. These are the components of the displacement along a different set of axes—one rotated 45.0°.