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Problem 31

Convert each number into scientific notation. $$0.154 \times 10^{4}$$

Problem 31

Multiply out each of the following. As you work out the problems, identify those exercises that are either a perfect square or the difference of two squares. $$(a-8)(a-8)$$

Problem 31

Multiply and simplify each of the following. Whenever possible, do the multiplication of two binomials mentally. $$(x+y)\left(x^{2}-x y+y^{2}\right)$$

Problem 32

Multiply and simplify each of the following. Whenever possible, do the multiplication of two binomials mentally. $$(m-n)\left(m^{2}+m n+n^{2}\right)$$

Problem 32

Convert each number into scientific notation. $$234.8 \times 10^{-3}$$

Problem 32

Simplify each of the following expressions as completely as possible. Final answers should be expressed with positive exponents only. (Assume that all variables represent positive quantities.) $$z^{3} z^{2} z^{-4} z^{-7}$$

Problem 33

Multiply out each of the following. As you work out the problems, identify those exercises that are either a perfect square or the difference of two squares. $$(a+8)(a-8)$$

Problem 33

Convert each number into scientific notation. $$28.40 \times 10^{6}$$

Problem 33

Simplify each of the following expressions as completely as possible. Final answers should be expressed with positive exponents only. (Assume that all variables represent positive quantities.) $$10^{-3} 10^{8}$$

Problem 33

Multiply and simplify each of the following. Whenever possible, do the multiplication of two binomials mentally. $$\left(x^{2}+x+1\right)\left(x^{2}+x-1\right)$$

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