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Chapter 7: Problem 16

Multiply as indicated. $$\frac{3 y^{2}+17 y+10}{3 y^{2}-22 y-16} \cdot \frac{y^{2}-4 y-32}{y^{2}-8 y-48}$$

Short Answer

Expert verified
The simplified form of the expression is \( \frac{(y + 5)(y + 4)}{(y - 6)(y + 8)} \)

Step by step solution

01

Factorizing Polynomials

Start by factorizing each polynomial in the numerator and the denominator. This will make the problem easier to work with. \[ \frac{3y^2 + 17y + 10}{3y^2 - 22y - 16} 脳 \frac{y^2 - 4y - 32}{y^2 - 8y - 48} \] factorizes to \[ \frac{(3y + 2)(y + 5)}{(3y + 2)(y - 8)} 脳 \frac{(y - 8)(y + 4)}{(y - 6)(y + 8)} \]
02

Cancelling Out Terms

Next, identify and cancel out the common terms that appear both in the numerator and the denominator. This helps in simplifying the expression. (3y + 2), (y - 8) can be cancelled out, thus the expression becomes \[ \frac{(y + 5)}{(1)} 脳 \frac{(y + 4)}{(y - 6)(y + 8)} \]
03

Multiplication

Multiply the fractions now that common terms have been cancelled out. This results in the simplified version of the expression. Floorman multiply the remaining terms, which results in the simplified version of the expression. \[ \frac{(y + 5)(y + 4)}{(y - 6)(y + 8)} \]

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Most popular questions from this chapter

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

Factor: \(25 x^{2}-81 .\) (Section 6.4, Example 1)

Describe two similarities between the following problems: $$ \frac{3}{8}+\frac{1}{8} \text { and } \frac{x}{x^{2}-1}+\frac{1}{x^{2}-1} $$

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

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