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18 tháng 2 2021
Bạn vào biểu tượng \(\Sigma\) để nhập biểu thức cho chính xác nhé
TT
0
LT
1
TM
20 tháng 6 2016
a) \(\left(x-1\right)^2-\left(x+3\right)^2+\left(x+4\right)\left(x-4\right)\)
\(=x^2-2x+1-\left(x^2+6x+9\right)+x^2-16\)
\(=x^2-2x+1-x^2-6x-9+x^2-16=-8x-24\)
b)
\(2\left(3x-2\right)^2-3\left(2x+5\right)^2-6\left(x+1\right)\left(x-1\right)\)
\(=2\left(9x^2-12x+4\right)-3\left(4x^2+20x+25\right)-6\left(x^2-1\right)\)
\(=18x^2-24x+8-12x^2-60x-75-6x^2+6=-84x-61\)
18 tháng 2 2021
a) Ta có: \(P=\left(\dfrac{x^2-1}{x^4-x^2+1}+\dfrac{2}{x^6+1}-\dfrac{1}{x^2+1}\right)\cdot\left(x^2-\dfrac{x^4+x^2-1}{x^4+x^2+1}\right)\)
\(=\left(\dfrac{\left(x^2-1\right)\left(x^2+1\right)}{\left(x^2+1\right)\left(x^4-x^2+1\right)}+\dfrac{2}{\left(x^2+1\right)\left(x^4-x^2+1\right)}-\dfrac{x^4-x^2+1}{\left(x^2+1\right)\left(x^4-x^2+1\right)}\right)\cdot\left(\dfrac{x^2\left(x^4+x^2+1\right)}{x^4+x^2+1}-\dfrac{x^4+x^2-1}{x^4+x^2+1}\right)\)
\(=\dfrac{x^4-1+2-x^4+x^2-1}{\left(x^2+1\right)\cdot\left(x^4-x^2+1\right)}\cdot\dfrac{x^6+x^4+x^2-x^4-x^2+1}{x^4+x^2+1}\)
\(=\dfrac{x^2}{\left(x^2+1\right)\left(x^4-x^2+1\right)}\cdot\dfrac{x^6+1}{x^4+x^2+1}\)
\(=\dfrac{x^2}{\left(x^2+1\right)\left(x^4-x^2+1\right)}\cdot\dfrac{\left(x^2+1\right)\left(x^4-x^2+1\right)}{x^4+x^2+1}\)
\(=\dfrac{x^2}{x^4+x^2+1}\)
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: \(\left(x-4\right)^2\left(x+4\right)-\left(x-4\right)\left(x+4\right)^2+3\left(x^2-16\right)\)
\(=\left(x-4\right)\left(x+4\right)\left(x-4-x-4\right)+3\left(x^2-16\right)\)
\(=\left(x^2-16\right)\left(-8\right)+3\left(x^2-16\right)\)
\(=-5\left(x^2-16\right)=-5x^2+80\)
K
0
9 tháng 8 2019
(x + 1)4 - 6(x + 1)2 - (x2 - 2)(x2 + 2)
= (x2 + 2x + 1)(x2 + 2x + 1) - 6(x2 + 2x + 1) - (x2 - 2)(x2 + 2)
= x4 + 2x3 + x2 + 2x3 + 4x2 + 2x + x2 + 2x + 1 - 6x2 - 12x - 6 - x4 + 4
= 4x3 - 8x + 1
GK
1
24 tháng 7 2023
\(=\dfrac{x+2}{\left(x-2\right)^2}:\left(\dfrac{6-x^2+x+x^2-4}{x\left(x-2\right)}\right)\)
\(=\dfrac{x+2}{\left(x-2\right)^2}\cdot\dfrac{x\left(x-2\right)}{x+2}=\dfrac{x}{x-2}\)
NM
1
5 tháng 12 2015
\(y=\frac{\frac{^x}{x^2}-x-6-x-\frac{1}{3}x^2-4x-15}{x^4}-2x^2+\frac{1}{3}x^2+11x+10b\)
\(y=\frac{-\left(5x^7-33x^6-30bx^5+x^3+18x^2+63x-3\right)}{3x^5}\)
(x + 1)^4 - 6(x + 1)^2 - (x^2 - 2)(x^2 + 2)
= (x^2 + 2x + 1)(x^2 + 2x + 1) - 6(x^2 + 2x + 1) - (x^2 - 2)(x^2 + 2)
= x^2.(x^2 + 2x + 1) + 2x.(x^2 + 2x + 1) + x^2 + 2x + 1 - (x^2 - 2)(x^2 + 2)
= x^4 + 2x^3 + x^2 + 2x^3 + 4x^2 + 2x + x^2 + 2x + 1 - 6x^2 - 12x - 6 - x^2 + 2^2
= 4x^3 - 8x - 1
\(\left(x+1\right)^4-6\left(x+1\right)^2-\left(x^2-2\right)\left(x^2+2\right)\)
\(=\left(x^2+2x-5\right)\left(x^2+2x+1\right)-x^4+2\)
\(=x^4+2x^3+x^2+2x^3+4x^2+2x-5x^2-10x-5-x^4+4\)
\(=4x^3-8x-1\)