I don't no how to race to power so i wrote some in words. But i need help. I don't know how to sovle it. The method i was taught is very confusing can someone show me like two diffent methods how to sovle this complex expression
(3x+1) power 2 - (x-3) power 2
2006-09-30 13:40:06 · 12 answers · asked by Agentj100 4 in Science & Mathematics ➔ Mathematics
No . Is not equal to zero
2006-09-30 13:46:31 · update #1
it's more like difference of squares
2006-09-30 13:47:53 · update #2
8x² + 12x - 8 IS NOT THE ANswer. i actually work it out and missed it. My teacher had wronged it.
2006-09-30 13:57:50 · update #3
The expression (3x+1)^2- (x-3)^2 =
2006-09-30 14:07:37 · update #4
Karpenisi did it right. That's the answer but i don't undertstand how he did it.
2006-09-30 14:17:55 · update #5
I do not know if you want to factor this or expand this. If you factor this, then
(3x + 1)² - (x - 3)²
It is an example of a difference of 2 squares. Why? Simply because (3x + 1)² is a square, (x - 3)² is a square, and that is the difference of two squares!. So how do we factor the difference of 2 squares? Here it is (If you want a proof, then find one in an algebra book):
a² - b² = (a + b)(a - b)
in other words, the difference of the squares of 2 numbers is equal to the product of their sum and difference. Thus,
(3x + 1)² - (x - 3)² = [(3x + 1) + (x - 3)][(3x + 1) - (x - 3)]
Or, when simplifying terms,
= (4x - 2)(2x + 4)
Since there are still common monomial factors,(2) then factor them out
= (2)(2x - 1)(2)(x + 2)
Multiply them
= 4(2x - 1)(x + 2)
There you go!.
If you want it the other way (the longer way),then expand them
(3x + 1)² - (x - 3)² = (9x² + 6x + 1) - (x² - 6x + 9)
Then simplify:
= 8x² + 12x - 8
Factor out the common monomial factor 4
= 4(2x² + 3x - 2)
then factor the trinomial
= 4(2x - 1)(x + 2)
^_^
2006-09-30 18:43:14 · answer #1 · answered by kevin! 5 · 2⤊ 0⤋
How about difference of squares. The problem is the difference between two squares. Let's simplify the problem and consider a^2-b^2 (this is what may have thrown you off - sorry). Due to algebra - a^2 - b^2 can be factored as follows:
a^2-b^2 = (a-b)(a+b)
Now, let a = (3x+1) and b = (x-3). Substitute into the right hand side of the above equation.
(3x + 1 -(x-3))(3x + 1 + x -3)
Now simplify the two expressions in the parentheses (I hope you know how to perform this).
(2x +4)(4x-2)
You can factor a 2 out of each parenthesis
2*(x+2)*2*(2x-1)
2*2 = 4
4(x+2)(2x-1)
The poster below me copied the above technique but she wrote x+3 instead of x-3 - making her solution a little off the mark. The bottom poster also copied me - but it's 0200 on the East Coast and I have to go to bed.
2006-09-30 14:13:52 · answer #2 · answered by Anonymous · 1⤊ 0⤋
What exactly do you need ? This is not an equality, just an expression, you can't solve something like that.
The only thing you could maybe do is to simplify it, in which case
you have
((3x-1)*(3x-1) - (x-3)*(x-3)) which is the same as
(9x² + 6x + 1) - ( x² - 6x + 9) which amounts to
9x² + 6x + 1 - x² + 6x - 9, simplified as
8x² + 12x - 8 if I am not terribly mistaken (shame on me if I am).
Other than that I don't know what you can make of this expression.
2006-09-30 13:50:46 · answer #3 · answered by Laton 1 · 0⤊ 1⤋
I will assume that you are trying to factor this expression (not solve it)
(3x+1)^2 - (x-3)^2
First recognize this as a difference of squares, and factor
=[(3x+1) + (x-3)] [(3x+1) - (x+3)]
Now remove the rounded brackets carefully
=[3x+1+x-3][3x+1-x-3]
Now collect any like terms to simplify.
=[4x-2][2x-2]
HOpe that's what you were looking for!
2006-09-30 14:20:05 · answer #4 · answered by whatthe 3 · 1⤊ 0⤋
(3x+1) power2 means (3x+1)times (3x+1) which is 9x squared plus 3x plus 3x plus1, which simplifies to 9x squared plus 6x plus1. (x-3)power 2 means (x-3) times (x-3) which works out at x squared -6x +9. If you take this axay from the first answer you get 8x squared +12x -8, and that's the answer.
2006-09-30 13:50:47 · answer #5 · answered by zee_prime 6 · 0⤊ 1⤋
Thus: (3x+1)^2- (x-3)^2 Foil method First group
(3x+1)* (3x+1)= 9x^2+3x+3x+1 Now you finish.
2006-09-30 13:48:08 · answer #6 · answered by Anonymous · 0⤊ 1⤋
9x"2 +6x +1 -
x"2 -6x + 9 =
8x"2 -8
and theres your answer !
sorry this isnt right
- (-) = + so the correct answer would be
8x"2 +12x - 8
so the post before this one is correct .
2006-09-30 13:50:53 · answer #7 · answered by shogunly 5 · 0⤊ 1⤋
enable variety raisins be x variety nuts be y the whole volume of the aggregate (nuts and raisins practice) will weight 15 pounds for this reason x+y=15 now, the whole value of the aggregate equals variety raisins circumstances its value plus variety nuts circumstances its value (and complete value of the aggregate is (15pounds * 4.25 in line with pound) for this reason 4.5x +3.75y= 4.25(15) follows the 2d question is an similar theory, merely diverse numbers
2016-10-16 03:00:33 · answer #8 · answered by Anonymous · 0⤊ 0⤋
(1**2 * (-3**2)) = 9
2006-09-30 13:58:24 · answer #9 · answered by walking 3 · 0⤊ 1⤋
You don't know how to write it either. In order to solve this you must let it equal to something i.e.0 or some other expression of x.
2006-09-30 13:45:16 · answer #10 · answered by Man_of_Aran 2 · 0⤊ 2⤋