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C2
2
12 tháng 7 2015
x3-12x-4x2+27
=(x3+27)-(12x+4x2)
=(x+3)(x2-3x+9)-4x(x+3)
=(x+3)(x2-3x+9-4x)
=(x+3)(x2-7x+9)
28 tháng 9 2018
\(x^3-12x-4x^2+27\)
\(=x^3+3x^2-7x^2-21x+9x+27\)
\(=x^2\left(x+3\right)-7x\left(x+3\right)+9\left(x+3\right)\)
\(=\left(x+3\right)\left(x^2-7x+9\right)\)
NT
1
24 tháng 10 2016
a) \(4x^2-8x+4-9\left(x-y\right)^2\)
\(=4\left(x^2-2x+1\right)-9\left(x-y\right)^2\)
\(=\left[2\left(x-1\right)\right]^2-\left[3\left(x-y\right)\right]^2\)
\(=\left(2x-2+3x-3y\right)\left(2x-2-3x+3y\right)\)
\(=\left(5x-3y-2\right)\left(3y-x-2\right)\)
b) \(x^3-4x^2+12x-27\)
\(=\left(x^3-27\right)-\left(4x^2-12x\right)\)
\(=\left(x-3\right)\left(x^2+3x+9\right)-4x\left(x-3\right)\)
\(=\left(x-3\right)\left(x^2-x+9\right)\)
NN
1
4 tháng 1 2019
\(x^4+4x^3-2x^2-12x+9\)
\(=x^4+3x^3+x^3+3x^2-5x^2-15x+3x+9\)
\(=x^3\left(x+3\right)+x^2\left(x+3\right)-5x\left(x+3\right)+3\left(x+3\right)\)
\(=\left(x+3\right)\left(x^3+x^2-5x+3\right)\)
\(=\left(x+3\right)\left(x^3+3x^2-2x^2-6x+x+3\right)\)
\(=\left(x+3\right)\left[x^2\left(x+3\right)-2x\left(x+3\right)+\left(x+3\right)\right]\)
\(=\left(x+3\right)\left(x+3\right)\left(x^2-2x+1\right)\)
\(=\left(x+3\right)^2\left(x-1\right)^2\)
17 tháng 8 2021
\(a)\)
\(4x^2-y^2+2x+y\)
\(=\left(4x^2-y^2\right)+\left(2x+y\right)\)
\(=\left(2x-y\right)\left(2x+y\right)+\left(2x+y\right)\)
\(=\left(2x+y\right)\left(2x-y+1\right)\)
\(b)\)
\(x^3+2x^2-6x-27\)
\(=x^3+5x^2+9x-3x^2-15x-27\)
\(=x\left(x^2+5x+9\right)-3\left(x^2+5x-9\right)\)
\(=\left(x-3\right)\left(x^2+5-9\right)\)
\(c)\)
\(12x^3+4x^2-27x-9\)
\(=\left(12x^3+4x^2\right)-\left(27x+9\right)\)
\(=4x^2\left(3x+1\right)-9\left(3x+1\right)\)
\(=\left(3x+1\right)\left(4x^2-9\right)\)
\(=\left(3x+1\right)[\left(2x\right)^2-3^2]\)
\(=\left(3x+1\right)\left(2x-3\right)\left(2x+3\right)\)
\(d)\)
\(16x^2+4x-y^2+y^2\)
\(=16x^2+4x\)
\(4x\left(4x+1\right)\)
11 tháng 10 2017
b)3x^2-18x+27=3x^2-9x-9x+27=3x*(x-3)-9*(x-3)=(x-3)*(3x-9)=(x-3)*3*(x-3)=3*(x-3)^2
c)x^3-4x^2-12x+27=(x+3)*(x^2-3x+9-4)=(x+3)*(x^2-3x+5)
d)27x^3-1/27=(3x-1/3)*(9x^2-x+1/9) (hang dt)
con a) voi e) mk chiu
DH
3
3 tháng 8 2021
\(16y^2-4x^2-12x-9=16y^2-\left(2x-3\right)^2\)
\(=\left(4y-2x+3\right)\left(4y+2x-3\right)\)
OP
9 tháng 8 2016
\(\left(x+5\right)\left(x-5\right)-\left(x-2\right)\left(x+7\right)=0\)
\(\left(x^2-5^2\right)-\left(x^2+7x-2x-14\right)=0\)
\(x^2-25-x^2-7x+2x+14=0\)
\(-5x=25-14\)
\(-5x=11\)
\(x=-\frac{11}{5}\)
***
\(9x^2-4-2\left(3x-2\right)^2=0\)
\(\left(3x\right)^2-2^2-2\left(3x-2\right)^2=0\)
\(\left(3x-2\right)\left(3x+2\right)-2\left(3x-2\right)^2=0\)
\(\left(3x-2\right)\left[\left(3x+2\right)-2\left(3x-2\right)\right]=0\)
\(\left(3x-2\right)\left(3x+2-6x+4\right)=0\)
\(\left(3x-2\right)\left(6-3x\right)=0\)
TH1:
\(3x-2=0\)
\(3x=2\)
\(x=\frac{2}{3}\)
TH2:
\(6-3x=0\)
\(3x=6\)
\(x=\frac{6}{3}\)
\(x=2\)
Vậy \(x=\frac{2}{3}\) hoặc \(x=2\)
***
\(12\left(3-4x\right)+7\left(4x-3\right)=0\)
\(12\left(3-4x\right)-7\left(3-4x\right)=0\)
\(\left(3-4x\right)\left(12-7\right)=0\)
\(5\left(3-4x\right)=0\)
\(3-4x=0\)
\(4x=3\)
\(x=\frac{3}{4}\)
***
\(x^2-4-2xy+y^2=\left(x-y\right)^2-2^2=\left(x-y-2\right)\left(x-y+2\right)\)
***
\(x^3-4x^2-12x+27=\left(x+3\right)\left(x^2-3x+9\right)-4x\left(x+3\right)=\left(x+3\right)\left(x^2-3x+9-4x\right)=\left(x+3\right)\left(x^2-7x+9\right)\)
***
\(3x^2-18x+27=3\left(x^2-2\times x\times3+3^2\right)=3\left(x-3\right)^2\)
***
\(A=-x^2+3x-4=-\left(x^2-2\times x\times\frac{3}{2}+\left(\frac{3}{2}\right)^2-\left(\frac{3}{2}\right)^2+4\right)=-\left[\left(x-\frac{3}{2}\right)^2+\frac{7}{4}\right]\)
\(\left(x-\frac{3}{2}\right)^2\ge0\)
\(\left(x-\frac{3}{2}\right)^2+\frac{7}{4}\ge\frac{7}{4}\)
\(-\left[\left(x-\frac{3}{2}\right)^2+\frac{7}{4}\right]\le-\frac{7}{4}< 0\)
Vậy A < 0 với mọi x (đpcm)
9 tháng 8 2016
1a (x+5)(x-5)-(x-2)(x+7) = 0
=> x2-25-(x2+5x-14) = 0
=> x2-25-x2-5x+14 = 0
=> -11-5x = 0
=> -5x = -11-0
=> -5x = -11
=> x = -11:5
=> x = \(\frac{-11}{5}\)
bài 2:
1) (x-y)2-4
3) 3(x2-6x+9)
TM
20 tháng 11 2016
a) \(\left(x+8\right)^2-2\left(x+8\right)\left(x-2\right)+\left(x-2\right)^2\)
\(=\left[\left(x+8\right)-\left(x-2\right)\right]^2\)
\(=\left(x+8-x+2\right)^2\)
\(=10^2\)
\(=2^2.5^2\)
b)\(x^3-4x^2-12x+27=\left(x^3+27\right)-\left(4x^2+12x\right)\)
\(=\left(x+3\right)\left(x^2-3x+9\right)-4x\left(x+3\right)\)
\(=\left(x+3\right)\left(x^2-3x+9-4x\right)\)
\(=\left(x+3\right)\left(x^2-7x+9\right)\)
c)\(x^3+6x^2+11x+6=x^3+x^2+5x^2+5x+6x+6\)
\(=x^2\left(x+1\right)+5x\left(x+1\right)+6\left(x+1\right)\)
\(=\left(x+1\right)\left(x^2+5x+6\right)\)
\(=\left(x+1\right)\left(x^2+2x+3x+6\right)\)
\(=\left(x+1\right)\left[x\left(x+2\right)+3\left(x+2\right)\right]\)
\(=\left(x+1\right)\left(x+2\right)\left(x+3\right)\)
d)\(x^3+6x^2-13x-42=x^3-3x^2+9x^2-27x+14x-42\)
\(=x^2\left(x-3\right)+9x\left(x-3\right)+14\left(x-3\right)\)
\(=\left(x-3\right)\left(x^2+9x+14\right)\)
\(=\left(x-3\right)\left(x^2+2x+7x+14\right)\)
\(=\left(x-3\right)\left[x\left(x+2\right)+7\left(x+2\right)\right]\)
\(=\left(x-3\right)\left(x+2\right)\left(x+7\right)\)
(x-3)(x^2-x+9)
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