91Ó°ÊÓ

Simplify. Assume that variables in the exponents represent nonzero integers and that \(x, y,\) and \(z\) are not \(0 .\) See Example 7 . $$ x^{5} \cdot x^{7 a} $$

Simplify each expression. $$ -5 y+4 y-18-y $$

Solve. A factored polynomial can be in many forms. For example, a factored form of \(x y-3 x-2 y+6\) is \((x-2)(y-3)\) Which of the following is not a factored form of \(x y-3 x-2 y+6 ?\) a. \((2-x)(3-y)\) b. \((-2+x)(-3+y)\) c. \((y-3)(x-2)\) d. \((-x+2)(-y+3)\)

Use the slope-intercept form of a line, \(y=m x+b,\) to find the slope of each line. See Section 3.4 $$ y=-2 x+7 $$

Multiply. See Section 5.4. $$ (x-3)(x+3) $$

Find the value of \(c\) that makes each trinomial a perfect square trinomial. Factor \(x^{6}-1\) completely, using the following methods from this chapter. A. Factor the expression by treating it as the difference of two squares, \(\left(x^{3}\right)^{2}-1^{2}\) B. Factor the expression by treating it as the difference of two squares, \(\left(x^{3}\right)^{2}-1^{2}\) C. Factor the expression by treating it as the difference of two squares, \(\left(x^{3}\right)^{2}-1^{2}\)

Multiply. See Section 5.4. $$ (x-4)(x+4) $$

Solve. Which factorization of \(12 x^{2}+9 x+3\) is correct? a. \(3\left(4 x^{2}+3 x+1\right)\) b. \(3\left(4 x^{2}+3 x-1\right)\) c. \(3\left(4 x^{2}+3 x-3\right)\) d. \(3\left(4 x^{2}+3 x\right)\)

Use the slope-intercept form of a line, \(y=m x+b,\) to find the slope of each line. See Section 3.4 $$ y=\frac{3}{2} x-1 $$

Simplify. Assume that variables in the exponents represent nonzero integers and that \(x, y,\) and \(z\) are not \(0 .\) See Example 7 . $$ x^{4 a} \cdot x^{7} $$