Rút gọn biểu thức sau:
A= (x - 3)2 - 2.( 2 - x).(x + 2) - (x+1)2.
help me please!!!!!
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DL
23 tháng 7 2019
a) \(\left(x^2-1\right)^3-\left(x^4+x^2+1\right)\left(x^2-1\right)=\left(x^2-1\right)\left[\left(x^2-1\right)^2-\left(x^4+x^2+1\right)\right]\)
\(=\left(x^2-1\right)\left(x^4-2x^2+1-x^4-x^2-1\right)=\left(x^2-1\right)\left(-3x^2\right)\)
\(=-3x^4+3x^2=3\left(x^2-x^4\right)=3\left(x-x^2\right)\left(x+x^2\right)=\left(3x-3x^2\right)\left(x+x^2\right).\)
DL
23 tháng 7 2019
b)\(\left(x^4-3x^2+9\right)\left(x^2+3-\left(3+x^2\right)\right)^3=\left(x^4-3x^2+9\right).0^3=0\)
c)\(\left(x-3\right)^3-\left(x-3\right)\left(x^2+3x+9\right)+6\left(x+1\right)^2=\left(x-3\right)^3-\left(x^3-3^3\right)+6\left(x^2+2x+1\right)\)
\(=\left(x-3\right)^3-\left[\left(x-3\right)^3+3.x.3.\left(x-3\right)\right]+6x^2+12x+6\)
\(=6x^2+12x+6-9x\left(x-3\right)=6x^2+12x+6-9x^2+27x\)
\(=39x-3x^2+6=3\left(13x-x^2+2\right).\)
6 tháng 7 2016
a) \(\left(x+1\right)^2-\left(x-1\right)^2-3\left(x+1\right)\left(x-1\right)\)
\(=x^2+2x+1-\left(x^2-2x+1\right)-3\left(x^2-1\right)\)
\(=x^2+2x+1-x^2+2x-1-3x^2+3\)
\(=4x+3\)
6 tháng 7 2016
b) \(5\left(x+2\right)\left(x-2\right)-\frac{1}{2}\left(6-8x\right)+17\)
\(=5\left(x^2-4\right)-3+4x+17\)
\(=5x^2-20-3+4x+17\)
\(=5x^2-6+4x\)
TN
1
1 tháng 7 2017
\(4x^2-28x+49=\left(2x\right)^2-2\cdot2x\cdot7+7^2=\left(2x-7\right)^2\)
Khi x=4 thì \(4x^2-28x+49=\left(2x-7\right)^2=\left(2\cdot4-7\right)^2=1\)
MN
0
6 tháng 9 2017
\(A=\left(\frac{1-x^3}{1-x}-x\right):\frac{1-x^2}{1-x-x^2+x^3}\)
\(=\frac{\left(1-x\right)\left(1+x+x^2\right)-x+x^2}{1-x}.\frac{\left(1-x\right)-x^2\left(1-x\right)}{\left(1-x\right)\left(1+x\right)}\)
\(=\frac{\left(1-x\right)\left(1+x+x^2\right)-x\left(1-x\right)}{1-x}.\frac{\left(1-x\right)\left(1-x^2\right)}{\left(1-x\right)\left(1+x\right)}\)
\(=\frac{\left(1-x\right)\left(1+x^2\right)}{1-x}.\frac{\left(1-x\right)\left(1-x\right)\left(1+x\right)}{\left(1-x\right)\left(1+x\right)}\)
\(=\left(1+x^2\right)\left(1-x\right)\)
\(=-x^3+x^2-x+1\)
6 tháng 9 2017
Ta có : \(A=\left(\frac{1-x^3}{1-x}-x\right):\frac{1-x^2}{1-x-x^2+x^3}\)
\(=\left(\frac{\left(1-x\right)\left(1+x+x^2\right)}{\left(1-x\right)}-x\right):\frac{\left(1-x\right)\left(1+x\right)}{\left(1-x\right)-\left(x^2-x^3\right)}\)
\(=\left(\left(1+x+x^2\right)-x\right):\frac{\left(1-x\right)\left(1+x\right)}{\left(1-x\right)-x^2\left(x-1\right)}\)
\(=\left(1+x^2\right):\frac{\left(1-x\right)\left(1+x\right)}{\left(1-x\right)\left(1-x^2\right)}\)
\(=\left(1+x^2\right):\frac{\left(1-x\right)\left(1+x\right)}{\left(1-x\right)\left(1-x\right)\left(x+1\right)}\)
\(=\left(1+x^2\right):\frac{1}{1-x}\)
\(=\left(1+x^2\right)\left(1-x\right)\)
\(A=\left(x-3\right)^2-2\left(2-x\right)\left(x+2\right)-\left(x+1\right)^2\)
\(=x^2-6x+9-2\left(4-x^2\right)-x^2-2x-1\)
\(=x^2-6x+9-8+2x^2-x^2-2x-1=2x^2-8x=2x\left(x-4\right)\)
sky sơn tùng giỏi toán quá z. hay kb với tui đi. rồi tui hỏi bài