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Chapter 5: Problem 66

Find each product. In each case, neither factor is a monomial. $$\left(\frac{1}{5} x+5\right)\left(\frac{3}{5} x-1\right)$$

Short Answer

Expert verified
\(\frac{3}{25}x^2 + \frac{14}{5}x - 5\)

Step by step solution

01

Distribute The First Terms

Multiply the first terms in each binomial: \((\frac{1}{5}x) * (\frac{3}{5}x) = \frac{3}{25}x^2\)
02

Distribute The Outer Terms

Multiply the outer terms in each binomial: \((\frac{1}{5}x) * -1 = -\frac{1}{5}x\)
03

Distribute The Inner Terms

Multiply the inner terms in each binomial: \(5 * (\frac{3}{5}x) = 3x\)
04

Distribute The Last Terms

Multiply the last terms in each binomial: \(5 * -1 = -5\)
05

Combine Like Terms

Add the resulting expressions from each step to get the final answer: \(\frac{3}{25}x^2 - \frac{1}{5}x + 3x - 5 = \frac{3}{25}x^2 + \frac{14}{5}x - 5 \)

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