## anonymous one year ago Factor 3x^2y^2 -xy^2-2y^2 Show your work

1. anonymous

you know that ^ means exponent right not multiply

2. anonymous

@nincompoop

3. anonymous

Yeah I need help solving it with steps

4. welshfella

Take out the GCF y^2

5. anonymous

$$\bf 3x^2y^2 -xy^2-2y^2\implies 3{\color{blue}{ x}}x{\color{blue}{ yy}}-x{\color{blue}{ yy}}-2{\color{blue}{ yy}}$$ take the common factor

6. anonymous

I'm really confused

7. anonymous

hmm $$\bf 3x^2y^2 -xy^2-2y^2\implies 3{x}x{\color{blue}{ yy}}-x{\color{blue}{ yy}}-2{\color{blue}{ yy}}$$ rather

8. anonymous

I don't even know where to start

9. welshfella

y^2(3x^2 - x - 2)

10. anonymous

Yes could you please show me the steps

11. DecentNabeel

$\mathrm{Factor}\:-2y^2+3x^2y^2-xy^2:\quad y^2\left(x-1\right)\left(3x+2\right)$

12. anonymous

hmm do you know how to take a common factor?

13. anonymous

Nope

14. anonymous

well.. then you may want to cover that firstly then

15. DecentNabeel

3x^2y^2 -xy^2-2y^2 take out y^2 $=y^2\left(3x^2-x-2\right)$ $\mathrm{Factor}\:3x^2-x-2:\quad \left(x-1\right)\left(3x+2\right)$ $=y^2\left(x-1\right)\left(3x+2\right)$

16. anonymous

3x^2y^2-xy^2-2y^2 -2y^2 +3x^2y^2-xy^2

17. anonymous

I just want to put this all together so it won't be difficult for you for your reference: Pulling out like terms : 5.1 Pull out like factors : 3x2y2 - xy2 - 2y2 = y2 • (3x2 - x - 2) Trying to factor by splitting the middle term 5.2 Factoring 3x2 - x - 2 The first term is, 3x2 its coefficient is 3 . The middle term is, -x its coefficient is -1 . The last term, "the constant", is -2 Step-1 : Multiply the coefficient of the first term by the constant 3 • -2 = -6 Step-2 : Find two factors of -6 whose sum equals the coefficient of the middle term, which is -1 . -6 + 1 = -5 -3 + 2 = -1 That's it Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -3 and 2 3x2 - 3x + 2x - 2 Step-4 : Add up the first 2 terms, pulling out like factors : 3x • (x-1) Add up the last 2 terms, pulling out common factors : 2 • (x-1) Step-5 : Add up the four terms of step 4 : (3x+2) • (x-1) Which is the desired factorization

18. anonymous

Thank you so much! Could you help on another

19. anonymous

Factor x^2+6x+9

20. DecentNabeel

$\mathrm{Factor}\:x^2+6x+9:\quad \left(x+3\right)^2$

21. anonymous

22. anonymous

& Try tipping those who help you out by rewarding them w/ a medal by clicking that 'best response' button.

23. anonymous

Ok thanks so muc!

24. anonymous

$$\Large\rm\color{darkviolet}{\sideset{_\star~^\star}{~~_\star~^\star}{_\star}\hspace{-56pt}\color{blueviolet}{\overset{^\star~~~_\star~~~_\star~~~^\star~~~_\star~~~^\star~~~^\star}{^\star~^\star~~~ \star~~~~_\star~\star~_\star~~~^\star}\hspace{-35pt}}\color{bluepurple}{\underset{^\star~~~^\star~~~\star~~~_\star~~~\star~~~^\star~~~_\star~~~}{\star}}}\hspace{96pt}\Large\rm\color{darkviolet}{\sideset{_\star~^\star}{~~~~~~^\star}{_\star}\hspace{-129pt}\color{blueviolet}{\overset{^\star~~~_\star~~~_\star~~~^\star~~~_\star~~~^\star~~~^\star}{^\star~^\star~~~ \star~^\star~~\star~~~_\star~~~^\star}\hspace{-159pt}}\color{bluepurple}{\underset{^\star~~~^\star~~~\star~~~_\star~~~\star~~~^\star~~~_\star~~~}{\star}}}\hspace{-165pt}\LARGE\rlap{\it\color{red}{W}\color{orange}{e}\color{gold}{l}\color{lime}{c}\color{blue}{o}\color{blueviolet}{m}\color{purple}{e}\color{orchid}{~t}\color{magenta}{o}\color{red}{~O}\color{orange}{p}\color{gold}{e}\color{lime}{n}\color{cyan}{S}\color{blue}{t}\color{blueviolet}{u}\color{purple}{d}\color{orchid}{y}\color{magenta}{!}}{\hspace{-1.5pt}\it\color{black}{Welcome~to~OpenStudy!}}$$ $$\it\color{charcoal}{~~~~Please~be~sure~to~read~OpenStudy's~terms~listed~within~the~following~links:}$$ $$~\hspace{1.5pt}\large\color{red}{_✧~}\huge\color{orange}{^✧~}\normalsize\color{gold}{✧~~}\Large\color{blue}{/)}\LARGE\color{blue}{_∧}\Large\color{blue}{/)~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~}\hspace{-3.5pt}\Large\color{blueviolet}{/)}\LARGE\color{blueviolet}{_∧}\Large\color{blueviolet}{/)~~~~}\hspace{-10pt}\large\color{gold}{^✧}\LARGE\color{orange}{_✧}\huge\color{yellow}{^✧}$$$$~~\Large\color{red}{~~_✧~~}\large\rm\color{blue}{O(}\Large\color{blue}{＾}\color{blue}{_ヮ}\hspace{-2pt}\Large\color{blue}{＾}\hspace{-2pt}\color{blue}{)o}\hspace{160pt}\Large\rm\color{blueviolet}{o(}\Large\hspace{-3pt}\color{blueviolet}{＾}\color{blueviolet}{_ヮ}\hspace{-2pt}\Large\color{blueviolet}{＾~}\hspace{-3pt}\large\color{blueviolet}{)O}\small\color{orange}{~_✧}\Large\color{gold}{~~^✧}\hspace{-235.7pt}\underset{\href{https:///openstudy.com/terms-and-conditions}{\hspace{0pt}\LARGE\it{\color{red}{\bigstar~T}}\color{orange}{e}\color{gold}{r}\color{lime}{m}\color{cyan}{s}\color{blue}{~a}\color{blueviolet}{n}\color{purple}{d}\color{orchid}{~C}\color{magenta}{o}\color{pink}{n}\color{red}{d}\color{orange}{i}\color{gold}{t}\color{lime}{i}\color{cyan}{o}\color{blue}{n}\color{blueviolet}{s}\color{red}{~\bigstar}}}{{\href{https:///openstudy.com/code-of-conduct}{\hspace{5.5pt}\large\it{\color{red}{\bigstar~C}}\color{orange}{o}\color{gold}{d}\color{lime}{e~}\color{cyan}{o}\color{blue}{f~}\color{blueviolet}{C}\color{purple}{o}\color{orchid}{n}\color{magenta}{d}\color{pink}{u}\color{red}{c}\color{orange}{t}\color{red}{~\bigstar}}}}$$ $$~\small\color{red}{~~~~~~~~_✧~~~~}\hspace{0pt}\large\rm\color{blue}{O(")(")~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~}\hspace{0pt}\large\rm\color{blueviolet}{(")(")O}\small\color{red}{~~~~~~✧}$$ $$\Large\color{green}{~~~~~⌒⌒⌒⌒⌒⌒⌒⌒⌒⌒⌒⌒⌒⌒⌒⌒⌒⌒⌒⌒⌒⌒⌒⌒⌒⌒⌒⌒⌒⌒⌒⌒⌒⌒}$$

25. anonymous

@DecentNabeel x^2 +3x +3x +9

26. anonymous

What's after

27. DecentNabeel

$\mathrm{Simplify}\:x^2+3x+3x+9:\quad x^2+6x+9$

28. anonymous

(X+3)(x+3)

29. DecentNabeel

$\mathrm{Simplify}\:\left(x+3\right)\left(x+3\right):\quad \left(x+3\right)^2$

30. DecentNabeel

Happy @kayleeq :)

31. anonymous

Wait what happened I'm sorry

32. anonymous

Factor x^2 -25

33. DecentNabeel

(x-5)(x+5)

34. anonymous

Is that all the steps

35. anonymous

Is a common factor for all of the x^2

36. DecentNabeel

x^2 -25 this formula a^2-b^2=(a-b)(a+b) x^2-5^2=(x-5)(x+5)

37. anonymous

Is that all of the steps though I'm so confused

38. DecentNabeel

tell me why confused

39. DecentNabeel

$x^2-25=\left(x+5\right)\left(x-5\right)$

40. anonymous

Is that the steps I don't know how to do this I've been at it for forever

41. DecentNabeel

you know a^2-b^2=(a-b)(a+b)

42. DecentNabeel

do you know this

43. anonymous

44. DecentNabeel

x^2 -25 use this formula:a^2-b^2=(a-b)(a+b): 25=5^2 x^2-5^2=(x-5)(x+5)

45. DecentNabeel

MATHEMATICAL FORMULAE Algebra 1. (a + b)2 = a2 + 2ab + b2; a2 + b2 = (a + b)2 − 2ab 2. (a − b)2 = a2 − 2ab + b2; a2 + b2 = (a − b)2 + 2ab 3. (a + b + c)2 = a2 + b2 + c2 + 2(ab + bc + ca) 4. (a + b)3 = a3 + b3 + 3ab(a + b); a3 + b3 = (a + b)3 − 3ab(a + b) 5. (a − b)3 = a3 − b3 − 3ab(a − b); a3 − b3 = (a − b)3 + 3ab(a − b) 6. a2 − b2 = (a + b)(a − b)

46. anonymous

Oooooooooo ok I got that see I just needed some explaination now only the second and third polynomial share a common factor is that correct it is x^2

47. DecentNabeel

yes

48. anonymous

Ok thank you sooooooooo much

49. DecentNabeel

welcome @kayleeq