Question

find each difference.

1. $(x^{2}+8x + 15)-(x^{2}-6x - 9)$
2. $(13mn^{2}-2nm^{2}+5n^{2})-(11mn^{2}-2n^{2})$
3. $(9y^{5}-6y^{3})-(6y^{5}-3y^{4}+5y^{3})$
4. $(10x^{2}-16x + 13)-(10x^{2}-15x - 10)$
5. the cost for a company to make a cell phone is $10x + 120$. the revenue that the company gets is $15x+75$. what is the total profit the company receives for selling $x$ cell phones?
6. if the same company in problem 5 sold 200 cell phones, what would their profit be?

optional reading: textbook lesson 16.1, check understanding & on your own 4, 6, 13 - 14; textbook lesson 16.2, check understanding & on your own 2, 9, 10, 12

Explanation:

Step1: Expand the first expression

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Step2: Combine like - terms

$$
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Step3: Expand the second expression

$$
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$$

Step4: Combine like - terms

$$
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$$

Step5: Expand the third expression

$$
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$$

Step6: Combine like - terms

$$
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$$

Step7: Expand the fourth expression

$$
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$$

Step8: Combine like - terms

$$
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$$

Step9: Calculate profit for question 5

Profit \(P=\text{Revenue}-\text{Cost}\). Given \(\text{Cost}=10x + 120\) and \(\text{Revenue}=15x+75\).

$$
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Step10: Calculate profit for question 6

Substitute \(x = 200\) into the profit formula \(P = 5x-45\) from question 5.

$$
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$$

Answer:

1. \(14x + 24\)
2. \(2mn^{2}-2nm^{2}+7n^{2}\)
3. \(3y^{5}+3y^{4}-11y^{3}\)
4. \(-x + 23\)
5. \(5x-45\)
6. \(955\)