SOLUTION: (2x + 1C3) - (2x-1C3) - 2(xC2) NOTE: C stands for combination

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Question 1134470: (2x + 1C3) - (2x-1C3) - 2(xC2)
NOTE: C stands for combination
Found 2 solutions by MathLover1, MathTherapy:
Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!

%282x+%2B+1C3%29+-+%282x-1C3%29+-+2%28xC2%29+
NOTE: C stands for combination
Remember, the formula to calculate combinations is nCr+=+n%21+%2F%28+r%21+%2A+%28n+-+r%29%21%29, where n represents the number of items, and r represents the number of items being chosen at a time.
=> 1C3 means n=1 and r=3
1C3+=+1%21+%2F%28+3%21+%2A+%281+-+3%29%21%29=0
since r=3 it can be chosen at a time from n=1 zero times
=> xC3 means n=x and r=2
xC2+=+x%21+%2F%28+2%21+%2A+%28x+-+2%29%21%29=x%5E2%2F2+-+x%2F2

then
%282x+%2B+0%29+-+%282x-0%29+-+2%28x%5E2%2F2+-+x%2F2%29
2x++-+2x-++%28x%5E2+-+x%29
-x%5E2+%2B+x


Answer by MathTherapy(10552) About Me  (Show Source):
You can put this solution on YOUR website!

(2x + 1C3) - (2x-1C3) - 2(xC2)
NOTE: C stands for combination
If this is: , and with matrix%281%2C3%2C+%22+%22%5Bn%5DC%5Br%5D%2C+%22=%22%2C+%22+%22%5Bn%5DP%5Br%5D%2Fr%21%29%29, we get:











%282x%284x%5E2+-+1%29+-+%282x+-+1%29%284x%5E2+-+10x+%2B+6%29+-+6x%5E2+%2B+6x%29%2F6



%288x%5E3+-+2x+-+8x%5E3+%2B+20x%5E2+-+12x+-++4x%5E2+%2B+10x+-+6+-+6x%5E2+%2B+6x%29%2F6

%288x%5E3+-+8x%5E3+%2B+20x%5E2+-+4x%5E2+-+6x%5E2+%2B+6x+-+12x+-+2x+%2B+10x+-+6%29%2F6

%2810x%5E2+%2B+2x+-+6%29%2F6 ======>