rút gọn C=(x-1)^3-(x+1)^3+6(x+1)
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1 tháng 10 2021
\(a,=x^2-6x+9-x^2+6x=9\\ b,=4x^2+4x+1-4x^2+9-4x-8=2\\ c,=\left(2x^2-2x-x+1\right):\left(x-1\right)\\ =\left(x-1\right)\left(2x-1\right):\left(x-1\right)=2x-1\)
1 tháng 10 2021
`a)(x-3)^2-x(x-6)`
`=x^2-6x+9-x^2+6x=9`
`b)(2x+1)^2-(3+2x)(2x-3)-4(x+2)`
`=4x^2+4x+1-(4x^2-9)-4x-8`
`=2`
`c)(2x^2-3x+1):(x-1)`
`=(2x^2-2x-x+1):(x-1)`
`=[2x(x-1)-(x-1)]:(x-1)`
`=2x-1`
P
Phong
CTVHS
22 tháng 7 2023
a) \(\dfrac{3x^2+6xy}{6x^2}=\dfrac{3x\left(x+2y\right)}{6x^2}=\dfrac{x+2y}{2x}\)
b) \(\dfrac{2x^2-x^3}{x^2-4}=\dfrac{x^2\left(2-x\right)}{\left(x+2\right)\left(x-2\right)}=\dfrac{-x^2}{x+2}\)
c) \(=\dfrac{x+1}{x^3+1}=\dfrac{x+1}{\left(x+1\right)\left(x^2+x+1\right)}=\dfrac{1}{x^2+x+1}\)
22 tháng 7 2023
`a, (3x^2+6xy)/(6x^2) = (x+2y)/(3x)`
`b, (2x^2-x^3)/(x^2-4) = (x^2(2-x))/((x-2)(x+2))`
`= -x^2/(x+2)`
`c, (x+1)/(x^3+1) = 1/(x^2-x+1)`
22 tháng 10 2023
1:
a: \(\left(2x-5\right)^2-4x\left(x+3\right)\)
\(=4x^2-20x+25-4x^2-12x\)
=-32x+25
b: \(\left(x-2\right)^3-6\left(x+4\right)\left(x-4\right)-\left(x-2\right)\left(x^2+2x+4\right)\)
\(=x^3-6x^2+12x-8-\left(x^3-8\right)-6\left(x^2-16\right)\)
\(=-6x^2+12x-6x^2+96=-12x^2+12x+96\)
c: \(\left(x-1\right)^2-2\left(x-1\right)\left(x+2\right)+\left(x+2\right)^2+5\left(2x-3\right)\)
\(=\left(x-1-x-2\right)^2+5\left(2x-3\right)\)
\(=\left(-3\right)^2+5\left(2x-3\right)\)
\(=9+10x-15=10x-6\)
2:
a: \(\left(2-3x\right)^2-5x\left(x-4\right)+4\left(x-1\right)\)
\(=9x^2-12x+4-5x^2+20x+4x-4\)
\(=4x^2+12x\)
b: \(\left(3-x\right)\left(x^2+3x+9\right)+\left(x-3\right)^3\)
\(=27-x^3+x^3-9x^2+27x-27\)
\(=-9x^2+27x\)
c: \(\left(x-4\right)^2\left(x+4\right)-\left(x-4\right)\left(x+4\right)^2+3\left(x^2-16\right)\)
\(=\left(x-4\right)\left(x+4\right)\left(x-4-x-4\right)+3\left(x^2-16\right)\)
\(=\left(x^2-16\right)\left(-8\right)+3\left(x^2-16\right)\)
\(=-5\left(x^2-16\right)=-5x^2+80\)
PA
16 tháng 9 2016
\(\left(x-1\right)^2-2\left(x-1\right)\left(x-3\right)+\left(x-3\right)^2=\left(x-1-x+3\right)^2=2^2=4\)
\(\left(2x+3\right)^2+\left(2x+3\right)\left(2x-6\right)+\left(x-3\right)^2=\left(2x+3\right)^2+2\left(2x+3\right)\left(x-3\right)+\left(x-3\right)^2=\left(2x+3+x-3\right)^2=\left(3x\right)^2=9x^2\)
AT
1
21 tháng 7 2023
\(P=\dfrac{\sqrt{x}}{\sqrt{x}-1}+\dfrac{2}{\sqrt{x}+3}+\dfrac{2-6\sqrt{x}}{\left(\sqrt{x}-1\right)\left(\sqrt{x}+3\right)}\)
\(=\dfrac{x+3\sqrt{x}+2\sqrt{x}-2+2-6\sqrt{x}}{\left(\sqrt{x}-1\right)\left(\sqrt{x}+3\right)}\)
\(=\dfrac{x-\sqrt{x}}{\left(\sqrt{x}-1\right)\left(\sqrt{x}+3\right)}=\dfrac{\sqrt{x}}{\sqrt{x}+3}\)
\(C=\left(x-1\right)^3-\left(x+1\right)^3+6\left(x+1\right)\)
\(=x^3-3x^2+3x-1-x^3-3x^2-3x-1+6x+6\)
\(=-6x^2+6x+4\)
`C = (x -1)^3 - (x+1)^3 + 6(x + 1)`
`= x^3 - 3x^2 + 3x - 1 - (x^3 + 3x^2 + 3x + 1) + 6x + 6`
`= x^3 - 3x^2 + 3x - 1 - x^3 - 3x^2 - 3x - 1 + 6x + 6`
`= - 6x^2 + 6x + 4`