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Chapter 0: Problem 101
Write each algebraic expression without parentheses. $$\frac{1}{3}(3 x)+[(4 y)+(-4 y)]$$
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Factor and simplify each algebraic expression. $$-8(4 x+3)^{-2}+10(5 x+1)(4 x+3)^{-1}$$
Why must \(a\) and \(b\) represent nonnegative numbers when we write \(\sqrt{a} \cdot \sqrt{b}=\sqrt{a b} ?\) Is it necessary to use this restriction in the case of \(\sqrt[3]{a} \cdot \sqrt[3]{b}=\sqrt[3]{a b} ?\) Explain.
Determine whether each statement makes sense or does not make sense, and explain your reasoning. Using my calculator, I determined that \(6^{7}=279,936,\) so 6 must be a seventh root of \(279,936\).
Determine whether each statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement. Some rational numbers are not positive.
Explain how to factor \(3 x^{2}+10 x+8\)
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