Question

lesson 17.3 homework
complete problems 1 - 6 for independent practice.
when you are finished, check the solutions with your teacher.
find each difference.

1. $(x^{2}+8x + 15)-(x^{2}-6x - 9)$
2. $(13mn^{2}-2nm^{2}+5n^{2})-(11mn^{2}-3n^{2})$
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?

Explanation:

Step1: Distribute the negative sign

$(x^2 + 8x + 15) - x^2 + 6x + 9$

Step2: Combine like terms

$(x^2 - x^2) + (8x + 6x) + (15 + 9)$
$= 14x + 24$

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Step1: Distribute the negative sign

$(13mn^2 - 2nm^2 + 5n^2) - 11mn^2 + 3n^2$

Step2: Combine like terms

$(13mn^2 - 11mn^2) - 2nm^2 + (5n^2 + 3n^2)$
$= 2mn^2 - 2m^2n + 8n^2$

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Step1: Distribute the negative sign

$(9y^5 - 6y^3) - 6y^5 + 3y^4 - 5y^3$

Step2: Combine like terms

$(9y^5 - 6y^5) + 3y^4 + (-6y^3 - 5y^3)$
$= 3y^5 + 3y^4 - 11y^3$

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Step1: Distribute the negative sign

$(10x^2 - 16x + 13) - 10x^2 + 15x + 10$

Step2: Combine like terms

$(10x^2 - 10x^2) + (-16x + 15x) + (13 + 10)$
$= -x + 23$

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Step1: Recall profit formula: Profit = Revenue - Cost

$\text{Profit} = (15x + 75) - (10x + 120)$

Step2: Distribute and combine like terms

$15x + 75 - 10x - 120 = 5x - 45$

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Step1: Substitute $x=200$ into profit formula

$\text{Profit} = 5(200) - 45$

Step2: Calculate the value

$1000 - 45 = 955$

Answer:

1. $14x + 24$
2. $2mn^2 - 2m^2n + 8n^2$
3. $3y^5 + 3y^4 - 11y^3$
4. $-x + 23$
5. $5x - 45$
6. $955$