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CHAPTER 6 REVIEW EXERCISES

CONCEPT CHECK EXERCISES

Determine each of the following as being either true or false. If it is false, explain why.

${(2 a - 3)}^{2} = 4 a^{2} - 9$
$2 x^{2} - 8 = 2 (x - 2) (x + 2)$
$6 x^{2} - 7 x + 1 = (3 x - 1) (2 x - 1)$
${(x + 2)}^{3} = x^{3} + 8$
$\frac{x^{2} + x - 2}{x^{2} + 3 x - 4} = \frac{x - 2}{3 x - 4}$
$\frac{x^{2} - y^{2}}{2 x + 1} \div (x + y) = \frac{x - y}{2 x + 1}$
$\frac{x}{y} - \frac{x + 1}{y + 1} = \frac{x + y}{y^{2} + y}$
$x = - 1$ is a solution to the equation $\frac{1}{x + 1} - \frac{2}{x} = - \frac{1}{x^{2} + x}$

PRACTICE AND APPLICATIONS

In Exercises 9–14, find the products by inspection. No intermediate steps should be necessary.

$3 a (4 x + 5 a)$
$- 7 x y (4 x^{2} - 7 y)$
$(3 a + 4 b) (3 a - 4 b)$
$(x - 4 z) (x + 4 z)$
$(b - 2) (b + 8)$
$(5 - y) (7 - y)$

In Exercises 15–46, factor the given expressions completely.

$5 s + 20 t$
$7 x - 28 y$
$a^{2} x^{2} + a^{2}$
$3 a x - 6 a x^{4} - 9 a$
$W^{2} b^{x + 2} - 144 b^{x}$

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