## lizz123 one year ago Add and subtract polynomials 10(u+v)+8(u-1)-3(u+6) @michele_laino

1. lizz123

What do I have to do first?

2. OregonDuck

Simplifying -10(u + v) + 8(u + -1) + -3(u + 6) = 0 (u * -10 + v * -10) + 8(u + -1) + -3(u + 6) = 0 (-10u + -10v) + 8(u + -1) + -3(u + 6) = 0 Reorder the terms: -10u + -10v + 8(-1 + u) + -3(u + 6) = 0 -10u + -10v + (-1 * 8 + u * 8) + -3(u + 6) = 0 -10u + -10v + (-8 + 8u) + -3(u + 6) = 0 Reorder the terms: -10u + -10v + -8 + 8u + -3(6 + u) = 0 -10u + -10v + -8 + 8u + (6 * -3 + u * -3) = 0 -10u + -10v + -8 + 8u + (-18 + -3u) = 0 Reorder the terms: -8 + -18 + -10u + 8u + -3u + -10v = 0 Combine like terms: -8 + -18 = -26 -26 + -10u + 8u + -3u + -10v = 0 Combine like terms: -10u + 8u = -2u -26 + -2u + -3u + -10v = 0 Combine like terms: -2u + -3u = -5u -26 + -5u + -10v = 0 Solving -26 + -5u + -10v = 0 Solving for variable 'u'. Move all terms containing u to the left, all other terms to the right. Add '26' to each side of the equation. -26 + -5u + 26 + -10v = 0 + 26 Reorder the terms: -26 + 26 + -5u + -10v = 0 + 26 Combine like terms: -26 + 26 = 0 0 + -5u + -10v = 0 + 26 -5u + -10v = 0 + 26 Combine like terms: 0 + 26 = 26 -5u + -10v = 26 Add '10v' to each side of the equation. -5u + -10v + 10v = 26 + 10v Combine like terms: -10v + 10v = 0 -5u + 0 = 26 + 10v -5u = 26 + 10v Divide each side by '-5'. u = -5.2 + -2v Simplifying u = -5.2 + -2v

3. lizz123

So, for the first part I have to distributive property. Correct?

4. OregonDuck

yes

5. Michele_Laino

here you have to apply the distributive propery of multiplication over addition, so we can write: $\Large \begin{gathered} 10\left( {u + v} \right) + 8\left( {u - 1} \right) - 3\left( {u + 6} \right) = \hfill \\ \hfill \\ = 10u + 10v + 8u - 8 - 3u - 18 = ... \hfill \\ \end{gathered}$ please simplify

6. Michele_Laino

Hint: next step is: $\Large \begin{gathered} 10\left( {u + v} \right) + 8\left( {u - 1} \right) - 3\left( {u + 6} \right) = \hfill \\ \hfill \\ = 10u + 10v + 8u - 8 - 3u - 18 = \hfill \\ \hfill \\ = \left( {10 + 8 - 3} \right)u + 10v - 8 - 18 = ... \hfill \\ \end{gathered}$

7. lizz123

I am so confused

8. Michele_Laino

why?

9. Michele_Laino

you have to combine like terms

10. lizz123

|dw:1434402027289:dw| Is that correct?

11. Michele_Laino

15 u is right 10 v is right whereas we have -18-8=-26, and not 18-8

12. lizz123

But 8-18 equals - 10

13. lizz123

nvm it is +10 So the answer is 15u + 10 v +10

14. Michele_Laino

yes! nevertheless, we have: 8(u-1)-3(u+3)=8u-8-3u-18, so the answer contains -8-18=-26

15. Michele_Laino

oops..-3(u+6)

16. lizz123

so the answer is: 15u + 10 v - 26?

17. Michele_Laino

that's right!

18. lizz123

oh now I get it thanks. ☺

19. Michele_Laino

:)

20. lizz123

so you know how there is a - sign right where: -3(u+6) don't you have to change the - sign to a + sign and the you have +3(-u-6) -3u - 18 which when I write the equation I have: 10 u + 10 v + 8 u - 8 - 3 u +18 ___________________ So 10 u + 8 u equals 18u which then you have to subtract by 3 which is 15u. Then I keep 10 v the same. -8 + 10 = 10 So the answer should be: 15 u + 10 v + 10 10 u + 10 v +8 u - 8 -3 u +18 ____________________ 15 u + 10 v + 10