91Ó°ÊÓ

Explain why the following factorization is not complete. Then finish the solution. $$ a x+a y+x+y=a(x+y)+x+y $$

When asked to factor \(81 t^{2}-16,\) one student answered \((9 t-4)(9 t+4),\) and another answered \((9 t+4)(9 t-4)\) Explain why both students are correct.

Search and Rescue. Two search-and-rescue teams leave base at the same time looking for a lost boy. The first team, on foot, heads north at \(2 \mathrm{mph}\) and the other, on horseback, south at \(4 \mathrm{mph}\). How long will it take them to search a distance of 21 miles between them?

Graph the line with the given characteristics. \(y\) -intercept \((0,-4) ;\) slope 3

On a test, when asked to find \((x-y)^{2},\) a student answered \(x^{2}-y^{2} .\) What error did the student make?

Graph the solution set of each inequality or system of inequalities on a rectangular coordinate system. $$ x \geq 2 $$

Factor Assume that \(n\) is a natural number. $$ 6 x^{2 n}+7 x^{n}-3 $$

Solve each inequality. Graph the solution set and write it using interval notation. $$ \frac{1}{4} p-\frac{1}{3} \leq p+2 $$

Simplify each expression. Assume there are no divisions by 0. $$ \left(\frac{\left(y^{5 x}\right)^{2}\left(y^{4 x}\right)^{4}}{\left(y^{2 x} \cdot y^{7}\right)^{-3}}\right)^{-2} $$