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1: \(\left(x-1\right)^3-x\left(x-2\right)^2+1\)
\(=x^3-3x^2+3x-1-x^3+4x^2-4x+1\)
\(=x^2-x\)
2: \(2x\left(3x+2\right)-3x\left(2x+3\right)\)
\(=6x^2+4x-6x^2-9x\)
=-5x
a: \(=\dfrac{5}{2x^2y}+\dfrac{2}{3xy}-\dfrac{y}{x^3}\)
\(=\dfrac{5\cdot3\cdot x}{6x^3y}+\dfrac{2\cdot2\cdot x^2}{6x^3y}-\dfrac{6y^2}{6x^3y}\)
\(=\dfrac{15x+4x^2-6y^2}{6x^3y}\)
b: \(=\dfrac{2x-7+3x+5}{10x-4}=\dfrac{5x-2}{10x-4}=\dfrac{1}{2}\)
c: \(=\dfrac{x^4-1-x^4+3x^2}{x^2-1}=\dfrac{3x^2-1}{x^2-1}\)
1: \(=6x^2+2x-15x-5-x^2+6x-9+4x^2+20x+25-27x^3-27x^2-9x-1\)
=-27x^3-18x^2+4x+10
2: =4x^2-1-6x^2-9x+4x+6-x^3+3x^2-3x+1+8x^3+36x^2+54x+27
=7x^3+37x^2+46x+33
5:
\(=25x^2-1-x^3-27-4x^2-16x-16-9x^2+24x-16+\left(2x-5\right)^3\)
\(=8x^3-60x^2+150-125+12x^2-x^3+8x-60\)
=7x^3-48x^2+8x-35
a, (x-1).(x-2).(x-3)
= (x2 - 2x - x + 2) . (x-3)
= (x2 - 3x + 2). (x-3)4
= x3 - 3x2 - 3x2 + 9x + 2x -6
= x3 - 6x2 + 11x -6
b) (x2 +x+1)(x2-1)(x2-x+1)
= (x4 - x2 + x3 - x+ x2 -1) . (x2 - x +1)
= (x4 + x3 -x -1) . (x2 - x +1)
= x6 - x5 + x4 + x5 - x4 + x3 - x2 + x -1
= x6 + x3 - x2 + x - 1
c) (2x-5)(4-3x)-(3x+11)(5-2x)-15(2x-5)
= (8x - 6x2 - 20 + 15x) - (15x-6x+55-22x) - 30x + 75
= 8x - 6x2 - 20 + 15x - 15x+6x-55+22x - 30x+75
= 6x-6x2 +55
d)(x2-2x+3)(3x-5)-(x2+x-1)(2x+7)
làm tương tự phần C
lưu ý trước dấu ngoặc là dấu trừ, khi phá ngoặc ra phải đổi dấu
a: \(=\dfrac{2\left(x+2\right)\left(x-1\right)}{x+2}=2x-2\)
b: \(=\dfrac{2x^3+x^2-6x^2-3x+2x+1}{2x+1}=x^2-3x+1\)
c: \(=\dfrac{x^3+2x^2-2x^2-4x+2x+4}{x+2}=x^2-2x+2\)
d: \(=\dfrac{x^2\left(x-3\right)}{x-3}=x^2\)
a: \(=\dfrac{4x-2+6x^2-6x+2x^2+1}{2x\left(2x-1\right)}=\dfrac{8x^2-2x-1}{2x\left(2x-1\right)}\)
a) \(\dfrac{1}{3x-2}-\dfrac{1}{3x+2}-\dfrac{3x-6}{9x^2-4}\)
\(=\dfrac{3x+2-3x+2-3x+6}{\left(3x-2\right)\left(3x+2\right)}\)
\(=\dfrac{-3x+10}{\left(3x-2\right)\left(3x+2\right)}\)
b) \(\dfrac{x+25}{2x^2-50}-\dfrac{x+5}{x^2-5x}-\dfrac{5-x}{2x^2+10x}\)
\(=\dfrac{x+25}{2\left(x-5\right)\left(x+5\right)}-\dfrac{x+5}{x\left(x-5\right)}+\dfrac{x-5}{2x\left(x+5\right)}\)
\(=\dfrac{x^2+25x-2\left(x+5\right)^2+\left(x-5\right)^2}{2x\left(x-5\right)\left(x+5\right)}\)
\(=\dfrac{x^2+25x-2x^2-20x-50+x^2-10x+25}{2x\left(x-5\right)\left(x+5\right)}\)
\(=\dfrac{-5x-25}{2x\left(x-5\right)\left(x+5\right)}\)
\(=\dfrac{-5\left(x+5\right)}{2x\left(x-5\right)\left(x+5\right)}=\dfrac{-5}{2x\left(x-5\right)}\)
c) Ta có: \(\dfrac{1-2x}{2x}-\dfrac{4x}{2x-1}-\dfrac{3}{2x-4x^2}\)
\(=\dfrac{-\left(2x-1\right)^2-8x^2+3}{2x\left(2x-1\right)}\)
\(=\dfrac{-\left(4x^2-4x+1\right)-8x^2+3}{2x\left(2x-1\right)}\)
\(=\dfrac{-4x^2+4x-1-8x^2+3}{2x\left(2x-1\right)}\)
\(=\dfrac{-12x^2+4x+2}{2x\left(2x-1\right)}\)
1) \(-6x^4+4x^3-2x^2\)
2) \(=x^2+4x-21-x^2-4x+5=-16\)
3) \(=6x^2-4x-x^2-4x-4=5x^2-8x-4\)
4) \(=2x^3-4x^2-8x-3x^2+6x+12=2x^3-7x^2-2x+12\)
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