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Chapter 7: Problem 17

Multiply as indicated. $$\left(y^{2}-9\right) \cdot \frac{4}{y-3}$$

Short Answer

Expert verified
The result of the multiplication is \(4y + 12\).

Step by step solution

01

Identify Difference of Squares

The binomial \(y^2 - 9\) is a difference of squares, because it can be written as \(y^2 - 3^2\).
02

Factor the Difference of Squares

Difference of squares can be factored into \((a+b)(a-b)\), so \(y^2 - 9\) becomes \((y-3)(y+3)\). Thus the expression becomes \((y-3)(y+3) \cdot \frac{4}{y-3}\).
03

Simplify the Expression

Notice that \((y-3)\) in the binomial and the denominator of the fraction can cancel each other out, the expression simplifies to \((y+3) \cdot 4 = 4y +12\)

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Most popular questions from this chapter

Add or subtract as indicated. Simplify the result, if possible. $$\frac{3}{x}+\frac{4}{x-6}$$

Will help you prepare for the material covered in the next section. If \(B=k W,\) find the value of \(k,\) in decimal form, using \(B=5\) and \(W=160\)

denominators are opposites, or additive inverses. Add or subtract as indicated. Simplify the result, if possible. $$\frac{9 x-1}{7 x-3}+\frac{6 x-2}{3-7 x}$$

denominators are opposites, or additive inverses. Add or subtract as indicated. Simplify the result, if possible. $$\frac{11}{x+7}-\frac{5}{-x-7}$$

Subtract: \(\frac{13}{15}-\frac{8}{45}\) (Section 1.2, Example 9)
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