Hi, there is a thing i don't understand while factorizing or .... they say that there are hidden 1 and the hidden 1 i don't understand them, can someone tell me where they are found? and how can i know if there is one? and do we multiply them or ....?
Thanks
2007-09-15 22:52:48 · 4 answers · asked by Anonymous in Science & Mathematics ➔ Mathematics
2x+1+5x(2x+1)-3x(2x+1)
2007-09-15 23:00:12 · update #1
Hi,
For 2x+1+5x(2x+1)-3x(2x+1), think of the first 2x+1 being inside a parentheses, just like the other (2x+1)s. Then there is an "understood 1" in front of the first 2x + 1 that just went into the parentheses, as follows:
Given: 2x+1+5x(2x+1)-3x(2x+1)
Re-write with parentheses around the 2x + 1 at the front:
(2x+1)+5x(2x+1)-3x(2x+1)
Now the "understood 1" can appear in front of it:
1(2x+1)..+..5x(2x+1)..-..3x(2x+1)
______......______.......______
Notice that all 3 of the underlined terms have a common factor of (2x+1), so it can be divided out of all of them. Notice this leaves behind the formerly invisible 1 in the first term.
1(2x+1).....5x(2x+1).....3x(2x+1)
----------..+..------------..-.------------- =
..(2x+1).......(2x+1)........(2x+1)
The (2x+1) divided out does not disappear, but is the GCF (greatest common factor) out front.
(2x+1)( 1 + 5x - 3x)
The second parentheses simplifies by combining like terms:
(2x+1)(1 + 2x)
I hope that helps explain the invisible one!! :-)
PS Likewise 3x + x = 4x because there's an invisible 1 in front of the x. Also x²(x) = x³ because there's an invisible 1 exponent on the second x to add together with the first exponent of 2.
2007-09-15 23:59:45 · answer #1 · answered by Pi R Squared 7 · 0⤊ 0⤋
As you know, any number or quantity that has no other apparent factors can always be factorised to, 1 times the quantity in question.
Like the first term in your question 2x+1 is really 1*(2x+1) and when the 2x+1 quantity is factored out then you are left with (1 + 5x - 3x) as the remaining factors:
2x+1+5x(2x+1)-3x(2x+1)=
1(2x+1)+5x(2x+1)-3x(2x+1)=
(2x+1)(1+5x-3x)=
(2x+1)(1+2x)=
(2x+1)²
Note the 1 in front of 2x+1 in the second step
we were only given the quantity 2x+1 but I factored it to 1 times 2x+1, it is always multiplied, and it also exists with the other terms, the 5x is 5x * 1 but I didn't need it there so I didn't use it.
2007-09-16 00:20:00 · answer #2 · answered by 037 G 6 · 0⤊ 0⤋
Sorry but the question is not clear. Why not post an actual example which you did not understand so that we can work together?
2007-09-15 22:58:02 · answer #3 · answered by Swamy 7 · 0⤊ 0⤋
the best way that we can understand is show your problem mathematically
2007-09-15 22:58:55 · answer #4 · answered by CPUcate 6 · 0⤊ 0⤋