Yes, that's right, you. :D
I would really appreciate it if you could tell me how to do this Algebra problem. Don't just give me the answer, but explain/show your work. I would really appreciate it, and 10 pts. to the fastest best answer!:
(3x + 2)^6
<3
2007-12-04 08:19:35 · 6 answers · asked by isabelle.the.insomniac 2 in Science & Mathematics ➔ Mathematics
What is to be done? Expanding the problem, or solving for roots?
How to expand:
(3x+2)(3x+2)(3x+2)^4
Multiply the first two first using FOIL:
(9x^2 + 12x + 4)(3x + 2)^4
We also know that (3x+2)^4 is (9x^2 + 12x + 4)^2 when expanded!
Therefore,
(9x^2 + 12x + 4)(9x^2 + 12x + 4)(9x^2 + 12x + 4)
Keep doing this method until you achieve your final answer.
2007-12-04 08:31:00 · answer #1 · answered by kromped 2 · 0⤊ 0⤋
I'm assuming you want us to expand the expression.
For this, I would use Pascal's Triangle, which, in the 7th row, has the numbers: 1, 6, 15, 20, 15, 6, 1
These are the multipliers for the terms you are going to multiply.
Consider your binomal expression (3x+2)^6 as (a+b)^6
The terms in the expanded expression will be:
a^6 + 6*a^5*b + 15*a^4*b^2 + 20*a^3*b^3 + 15*a^2*b*4 + 6*a*b^5 + b^6
So, you get:
729x^6 + 2916x^5 + 4860x^4 + 4320x^3 + 2160x^2 + 576x + 64
2007-12-04 16:29:23 · answer #2 · answered by lhvinny 7 · 0⤊ 0⤋
What are you trying to do with the question? Expand it?
Using bionomial expansion this becomes
(3x+2)^6
=(3x)^6 + 6*(3x)^5*(2) + 15*(3x)^4*(2)^2 + 20*(3x)^3*(2)^3 + 15(3x)^2*(2)^4 + 6*(3x)*(2)^5 + (2)^6
= 729x^6 + 2916x^5 + 4860x^4 + 4320x^3 + 2160x^2 + 576x + 64
2007-12-04 16:32:02 · answer #3 · answered by Ian 6 · 0⤊ 0⤋
I'm assuming the people above and below me are thinking a little too hard.
is your question to solve (3x + 2)^6<3 ? if so this is how:
Take the sixth root of both sides
3x + 2 < sixthroot(3)
subtract two from both sides:
3x < sixthroot(3) - 2
divide both sides by 3:
x < (1/3)sixthroot(3) - 2/3
to find out what the sixthroot of three is, use the button on your calculator with an x infront of the radican.
push 6, push that button, push 3, enter.
2007-12-04 16:29:48 · answer #4 · answered by KEYNARDO 5 · 0⤊ 1⤋
If (3x+2)^6 < 3 then 3x+2 < 3^(1/6) and thus
x < (3^(1/6) - 2)/3. P.S. am I the only person who sees that this is an inequality problem...sheople all !!!!!!!!!
2007-12-04 16:32:16 · answer #5 · answered by Anonymous · 0⤊ 0⤋
(3x+2)(3x+2)(3x+2)(3x+2)(3x+2)(3x+2)=(9x^2 + 12x +4)^3
(9x^2 + 12x +4)(9x^2 + 12x +4)(9x^2 + 12x +4) ~>and keep "foil"-ing....its more of a pain in the *** than anything....just takes a long time....
2007-12-04 16:30:12 · answer #6 · answered by Liberal & Proud! 5 · 1⤊ 0⤋