Chapter 5

For Problems \(1-10\), find the indicated products by applying the distributive property; for example, $$ \begin{aligned} (x+1)(y+5) &=x(y)+x(5)+1(y)+1(5) \\ &=x y+5 x+y+5 \end{aligned} $$ $$ (x+2)(y+3) $$

For Problems \(1-30\), multiply using the properties of exponents to help with the manipulation. $$ (5 x)(9 x) $$

For Problems \(1-30\), evaluate each numerical expression. $$ 3^{-2} $$

For Problems \(1-40\), perform the divisions. (Objective 1) $$ \left(x^{2}+16 x+48\right) \div(x+4) $$

For Problems \(1-24\), divide the monomials. $$ \frac{x^{10}}{x^{2}} $$

For Problems \(1-8\), determine the degree of each polynomial. $$ 7 x^{2} y+6 x y $$

For Problems \(1-10\), find the indicated products by applying the distributive property; for example, $$ \begin{aligned} (x+1)(y+5) &=x(y)+x(5)+1(y)+1(5) \\ &=x y+5 x+y+5 \end{aligned} $$ $$ (x+3)(y+6) $$

For Problems \(1-30\), multiply using the properties of exponents to help with the manipulation. $$ (7 x)(8 x) $$

For Problems \(1-30\), evaluate each numerical expression. $$ 2^{-5} $$

For Problems \(1-40\), perform the divisions. (Objective 1) $$ \left(x^{2}+15 x+54\right) \div(x+6) $$

For Problems \(1-24\), divide the monomials. $$ \frac{x^{12}}{x^{5}} $$

For Problems \(1-8\), determine the degree of each polynomial. $$ 4 x y-7 x $$

For Problems \(1-10\), find the indicated products by applying the distributive property; for example, $$ \begin{aligned} (x+1)(y+5) &=x(y)+x(5)+1(y)+1(5) \\ &=x y+5 x+y+5 \end{aligned} $$ $$ (x-4)(y+1) $$

For Problems \(1-30\), multiply using the properties of exponents to help with the manipulation. $$ \left(3 x^{2}\right)(7 x) $$

For Problems \(1-30\), evaluate each numerical expression. $$ 4^{-3} $$

For Problems \(1-40\), perform the divisions. (Objective 1) $$ \left(x^{2}-5 x-14\right) \div(x-7) $$

For Problems \(1-24\), divide the monomials. $$ \frac{4 x^{3}}{2 x} $$

For Problems \(1-8\), determine the degree of each polynomial. $$ 5 x^{2}-9 $$

For Problems \(1-10\), find the indicated products by applying the distributive property; for example, $$ \begin{aligned} (x+1)(y+5) &=x(y)+x(5)+1(y)+1(5) \\ &=x y+5 x+y+5 \end{aligned} $$ $$ (x-5)(y+7) $$

For Problems \(1-30\), multiply using the properties of exponents to help with the manipulation. $$ (9 x)\left(4 x^{3}\right) $$

For Problems \(1-30\), evaluate each numerical expression. $$ 5^{-2} $$

For Problems \(1-40\), perform the divisions. (Objective 1) $$ \left(x^{2}+8 x-65\right) \div(x-5) $$

For Problems \(1-24\), divide the monomials. $$ \frac{8 x^{5}}{4 x^{3}} $$

For Problems \(1-8\), determine the degree of each polynomial. $$ 8 x^{2} y^{2}-2 x y^{2}-x $$

For Problems \(1-10\), find the indicated products by applying the distributive property; for example, $$ \begin{aligned} (x+1)(y+5) &=x(y)+x(5)+1(y)+1(5) \\ &=x y+5 x+y+5 \end{aligned} $$ $$ (x-5)(y-6) $$

For Problems \(1-30\), multiply using the properties of exponents to help with the manipulation. $$ (-3 x y)(2 x y) $$

For Problems \(1-30\), evaluate each numerical expression. $$ \left(\frac{3}{2}\right)^{-1} $$

For Problems \(1-40\), perform the divisions. (Objective 1) $$ \left(x^{2}+11 x+28\right) \div(x+3) $$

For Problems \(1-24\), divide the monomials. $$ \frac{-16 n^{6}}{2 n^{2}} $$

For Problems \(1-8\), determine the degree of each polynomial. $$ 5 x^{3}-x^{2}-x+3 $$

For Problems \(1-10\), find the indicated products by applying the distributive property; for example, $$ \begin{aligned} (x+1)(y+5) &=x(y)+x(5)+1(y)+1(5) \\ &=x y+5 x+y+5 \end{aligned} $$ $$ (x-7)(y-9) $$

For Problems \(1-30\), multiply using the properties of exponents to help with the manipulation. $$ (6 x y)(-3 x y) $$

For Problems \(1-30\), evaluate each numerical expression. $$ \left(\frac{3}{4}\right)^{-2} $$

For Problems \(1-40\), perform the divisions. (Objective 1) $$ \left(x^{2}+11 x+15\right) \div(x+2) $$

For Problems \(1-24\), divide the monomials. $$ \frac{-54 n^{8}}{6 n^{4}} $$

For Problems \(1-8\), determine the degree of each polynomial. $$ 8 x^{4}-2 x^{2}+6 $$

For Problems \(1-10\), find the indicated products by applying the distributive property; for example, $$ \begin{aligned} (x+1)(y+5) &=x(y)+x(5)+1(y)+1(5) \\ &=x y+5 x+y+5 \end{aligned} $$ $$ (x+2)(y+z+1) $$

For Problems \(1-30\), multiply using the properties of exponents to help with the manipulation. $$ \left(-2 x^{2} y\right)(-7 x) $$

For Problems \(1-30\), evaluate each numerical expression. $$ \frac{1}{2^{-4}} $$

For Problems \(1-40\), perform the divisions. (Objective 1) $$ \left(x^{2}-4 x-39\right) \div(x-8) $$

For Problems \(1-24\), divide the monomials. $$ \frac{72 x^{3}}{-9 x^{3}} $$

For Problems \(1-8\), determine the degree of each polynomial. $$ 5 x y $$

For Problems \(1-10\), find the indicated products by applying the distributive property; for example, $$ \begin{aligned} (x+1)(y+5) &=x(y)+x(5)+1(y)+1(5) \\ &=x y+5 x+y+5 \end{aligned} $$ $$ (x+4)(y-z+4) $$

For Problems \(1-30\), multiply using the properties of exponents to help with the manipulation. $$ \left(-5 x y^{2}\right)(-4 y) $$

For Problems \(1-30\), evaluate each numerical expression. $$ \frac{1}{3^{-1}} $$

For Problems \(1-40\), perform the divisions. (Objective 1) $$ \left(x^{2}-9 x-30\right) \div(x-12) $$

For Problems \(1-24\), divide the monomials. $$ \frac{84 x^{5}}{-7 x^{5}} $$

For Problems \(1-8\), determine the degree of each polynomial. $$ -7 x+4 $$

For Problems \(1-10\), find the indicated products by applying the distributive property; for example, $$ \begin{aligned} (x+1)(y+5) &=x(y)+x(5)+1(y)+1(5) \\ &=x y+5 x+y+5 \end{aligned} $$ $$ (2 x+3)(3 y+1) $$

For Problems \(1-30\), multiply using the properties of exponents to help with the manipulation. $$ \left(4 a^{2} b^{2}\right)(-12 a b) $$