Question

simplify.$(2u^{2}-8u+6)+(-6u^{2}-3u-9)-(-u^{2}-5u-5)$question 2 of 9divide.$\frac{8v^{4}+15v^{3}}{2v^{3}}$simplify your answer as much as possible.question 3 of 9divide.$(11z^{7}x-8z^{7}x^{3})div(-2z^{5}x^{2})$simplify your answer as much as possible.question 4 of 9use the distributive property to remove the parentheses.$9c^{2}(3c^{4}-5)$simplify your answer as much as possible.

Explanation:

Question 1

Step1: Remove parentheses

$(2u^2 - 8u + 6) + (-6u^2 - 3u - 9) - (-u^2 - 5u - 5) = 2u^2 - 8u + 6 - 6u^2 - 3u - 9 + u^2 + 5u + 5$

Step2: Combine like $u^2$ terms

$2u^2 - 6u^2 + u^2 = (2 - 6 + 1)u^2 = -3u^2$

Step3: Combine like $u$ terms

$-8u - 3u + 5u = (-8 - 3 + 5)u = -6u$

Step4: Combine constant terms

$6 - 9 + 5 = 2$

Question 2

Step1: Split the fraction

$\frac{8v^4 + 15v^3}{2v^3} = \frac{8v^4}{2v^3} + \frac{15v^3}{2v^3}$

Step2: Simplify each term

$\frac{8v^4}{2v^3} = 4v$, $\frac{15v^3}{2v^3} = \frac{15}{2}$

Question 3

Step1: Split the division

$(11z^7x - 8z^7x^3) \div (-2z^5x^2) = \frac{11z^7x}{-2z^5x^2} - \frac{8z^7x^3}{-2z^5x^2}$

Step2: Simplify each term

$\frac{11z^7x}{-2z^5x^2} = -\frac{11}{2}z^{2}x^{-1} = -\frac{11z^2}{2x}$, $\frac{8z^7x^3}{2z^5x^2} = 4z^2x$

Question 4

Step1: Apply distributive property

$9c^2(3c^4 - 5) = 9c^2 \cdot 3c^4 - 9c^2 \cdot 5$

Step2: Simplify each product

$9c^2 \cdot 3c^4 = 27c^{6}$, $9c^2 \cdot 5 = 45c^2$

Answer:

1. $-3u^2 - 6u + 2$
2. $4v + \frac{15}{2}$
3. $-\frac{11z^2}{2x} + 4z^2x$
4. $27c^6 - 45c^2$