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\(\left(3x^2-x-1\right)\left(3x^2+x-1\right)\)
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LC
29 tháng 6 2017
\(=3x^2\left(x^2-1\right)+\left(x^8-3x^4+3x^2-1\right)-\left(x^8-1\right)\)
\(=3x^4-3x^2+x^8-3x^4+3x^2+1-x^8+1\)
\(=2\)
20 tháng 8 2019
=2 nha ban
(con cach lam ban nhan dang thuc len rui rut gon lai)
2 tháng 9 2019
\(a,\left(-4xy-5\right)\left(5-4xy\right)=\left(4xy+5\right)\left(4xy-5\right).\)
\(=\left(4xy\right)^2-5^2=16x^2y^2-25\)
\(b,\left(a^2b+ab^2\right)\left(ab^2-a^2b\right)=\left(ab^2+a^2b\right)\left(ab^2-a^2b\right)\)
\(=\left(ab^2\right)^2-\left(a^2b\right)^2=a^2b^4-a^4b^2\)
\(c,\left(3x-4\right)^2+2\left(3x-4\right)\left(4-x\right)+\left(4-x\right)^2\)
\(=\left[\left(3x-4\right)+\left(4-x\right)\right]^2\)
\(=\left(3x-4+4-x\right)^2=\left(2x\right)^2=4x^2\)
\(d,\left(a^2+ab+b^2\right)\left(a^2-ab+b^2\right)-\left(a^4+b^4\right)\)
\(=\left[\left(a^2+b^2\right)+ab\right]\left[\left(a^2+b^2\right)-ab\right]-\left(a^4+b^4\right)\)
\(=\left(a^2+b^2\right)^2-\left(ab\right)^2-a^4-b^4\)
\(=a^4+2a^2b^2+b^4-a^2b^2-a^4-b^4=a^2b^2\)
VN
1
2T
14 tháng 8 2019
\(\left(x^2-x+1\right)\left(x^2+x+1\right)\)
\(=\left(x^2+1\right)^2-x^2\)
\(=x^4+2x^2+1-x^2\)
\(=x^4+x^2+1\)
Q
23 tháng 6 2017
a) \(x\left(x-1\right)\left(x+1\right)-\left(x+1\right)\left(x^2-x+1\right)\)
\(=\left(x+1\right)\cdot\left[x\cdot\left(x-1\right)-\left(x^2-x+1\right)\right]\)
\(=\left(x+1\right)\left(x^2-x-x^2+x-1\right)\)
\(=\left(x+1\right)\cdot\left(-1\right)\)
\(=-1\left(x+1\right)\)
b) \(\left(x-1\right)^3-\left(x+2\right)\left(x^2-2x+4\right)+3\left(x+4\right)\left(x-4\right)\)
\(=x^3-3x^2+3x-1-\left(x^3+8\right)+\left(3x+12\right)\left(x-1\right)\)
\(=x^3-3x^2+3x-1-\left(x^3+8\right)+3x^2-3x+12x-12\)
\(=x^3-1-x^3-8+12x-12\)
\(=-21+12x\)
c) \(3x^2\left(x+1\right)\left(x-1\right)+\left(x^2-1\right)^3-\left(x^2-1\right)\left(x^4+x^2+1\right)\)
\(=3x^2\left(x^2-1\right)+x^6-3x^4+3x^2-1-\left(x^6-1\right)\)
\(=3x^4-3x^2+x^6-3x^4+3x^2-1-x^6+1\)
\(=0\)
TA
1 tháng 6 2021
VT = `[ 2/(3x) -2/(x+1) (x+1)/(3x) -x-1)]: (x-1)/x`
`=[2/(3x)-2/(x+1) . ((x+1)-3x(x+1))/(3x) ] . x/(x-1)`
`= [2/(3x) + 2/(x+1) ((3x-1)(x+1))/(3x) ] . x/(x-1)`
`= [ 2/(3x) + (2(3x-1))/(3x) ] . x/(x-1)`
`= (6x)/(3x) . x/(x-1)`
`= 2 . x/(x-1)`
`= (2x)/(x-1)`
H9
HT.Phong (9A5)
CTVHS
6 tháng 7 2023
3) \(\left(x+3\right)^2+\left(x-2\right)^2-2\left(x+3\right)\left(x-2\right)\)
\(=\left(x+3\right)^2-2\left(x+3\right)\left(x-2\right)+\left(x-2\right)^2\)
\(=\left[\left(x+3\right)-\left(x-2\right)\right]^2\)
\(=\left(x+3-x+2\right)^2\)
\(=5^2=25\)
4) \(\left(3x-5\right)^2-2\left(3x-5\right)\left(3x+5\right)+\left(3x+5\right)^2\)
\(=\left[\left(3x-5\right)-\left(3x+5\right)\right]^2\)
\(=\left(3x-5-3x-5\right)^2\)
\(=\left(-10\right)^2\)
\(=100\)
\(\left(3x^2-x-1\right)\left(3x^2+x-1\right)\)
\(=\left(3x^2-1\right)^2-x^2\)
\(=9x^4-6x^2+1-x^2\)
\(=9x^4-7x^2+1\)