thực hiện phép chia :
[ 10x^2 (x+2)^3 -8x^3(x+2)^2+4x(x+2)^3] : 2x(x+2)^2
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24 tháng 2 2023
a: \(=\dfrac{2x^4+x^3-5x^2-3x-3}{x^2-3}\)
\(=\dfrac{2x^4-6x^2+x^3-3x+x^2-3}{x^2-3}\)
\(=2x^2+x+1\)
b: \(=\dfrac{x^5+x^2+x^3+1}{x^3+1}=x^2+1\)
c: \(=\dfrac{2x^3-x^2-x+6x^2-3x-3+2x+6}{2x^2-x-1}\)
\(=x+3+\dfrac{2x+6}{2x^2-x-1}\)
d: \(=\dfrac{3x^4-8x^3-10x^2+8x-5}{3x^2-2x+1}\)
\(=\dfrac{3x^4-2x^3+x^2-6x^3+4x^2-2x-15x^2+10x-5}{3x^2-2x+1}\)
\(=x^2-2x-5\)
1 tháng 11 2021
a: \(=\dfrac{x^2-5x+x+4}{x\left(x-2\right)}=\dfrac{x^2-4x+4}{x\left(x-2\right)}=\dfrac{x-2}{x}\)
b: \(=\dfrac{x^2-6x+9+4x^2+8x-4x^2-8x}{\left(x-3\right)\left(x+2\right)}\)
\(=\dfrac{x-3}{x+2}\)
1 tháng 11 2021
a) \(=\dfrac{x\left(x-5\right)+x+4}{x\left(x-2\right)}=\dfrac{x^2-4x+4}{x\left(x-2\right)}=\dfrac{\left(x-2\right)^2}{x\left(x-2\right)}=\dfrac{x-2}{x}\)
b) \(=\dfrac{\left(x-3\right)^2+4x\left(x+2\right)-8x-4x^2}{\left(x+2\right)\left(x-3\right)}=\dfrac{x^2-6x+9+4x^2+8x-8x-4x^2}{\left(x+2\right)\left(x-3\right)}\)
\(=\dfrac{x^2-6x+9}{\left(x+2\right)\left(x-3\right)}=\dfrac{\left(x-3\right)^2}{\left(x+2\right)\left(x-3\right)}=\dfrac{x-3}{x+2}\)
18 tháng 11 2021
\(Bài1:\\ a,\left(4x-1\right)\left(2x^2-x-1\right)=4x\left(2x^2-x-1\right)-\left(2x^2-x-1\right)=8x^3-4x^2-4x-2x^2+x+1=8x^3-6x^2-3x+1\\ b,\left(4x^3+8x^2-2x\right):2x\\ =2x\left(2x^2+4x-1\right):2x\\ =2x^2+4x-1\)
\(Bài2:\\ a,2x^3-8x^2+8x=2x\left(x^2-4x+4\right)=2x\left(x-2\right)^2\\ b,2xy+2x+yz+z=2x\left(y+1\right)+z\left(y+1\right)=\left(y+1\right)\left(2x+z\right)\\ c,x^2+2x+1-y^2=\left(x+1\right)^2-y^2=\left(x-y+1\right)\left(x+y+1\right)\)
KV
2 tháng 5 2023
a) 4x²(x² - 5x + 2)
= 4x².x² - 4x².5x + 4x².2
= 4x⁴ - 20x³ + 8x²
b) (2x² - 5x + 3) : (2x - 3)
= (2x² - 3x - 2x + 3) : (2x - 3)
= [(2x² - 3x) - (2x - 3)] : (2x - 3)
= [x(2x - 3) - (2x - 3)] : (2x - 3)
= (2x - 3)(x - 1) : (2x - 3)
= x - 1
\(\dfrac{10x^2\left(x+2\right)^3-8x^3\left(x+2\right)^2+4x\left(x+2\right)^3}{2x\left(x+2\right)^2}\)
\(=\dfrac{10x^2\left(x+2\right)^3}{2x\left(x+2\right)^2}-\dfrac{8x^3\left(x+2\right)^2}{2x\left(x+2\right)^2}+\dfrac{4x\left(x+2\right)^3}{2x\left(x+2\right)^2}\)
\(=\dfrac{2x\cdot\left(x+2\right)^2\cdot5x\cdot\left(x+2\right)}{2x\left(x+2\right)^2}-\dfrac{2x\cdot\left(x+2\right)^2\cdot4x^2}{2x\left(x+2\right)^2}+\dfrac{2x\left(x+2\right)^2\cdot2\cdot\left(x+2\right)}{2x\left(x+2\right)^2}\)
\(=5x\left(x+2\right)-4x^2+2\left(x+2\right)\)
\(=5x^2+10x-4x^2+2x+4\)
\(=x^2+12x+4\)