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1. 20\(x^2y^3\) : 4x\(y^2\) = 5xy
2. \(\dfrac{-1}{2}x^4y^4\) : \(\dfrac{2}{3}x^2y^2\) = \(\dfrac{-3}{4}x^2y^2\)
3. \(\left(-xy\right)^6:\left(-xy\right)^2=\left(-xy\right)^2\) = xy
4. 27\(x^2y^3z^4:\left(-3xyz\right)^2\) = 27\(x^2y^3z^4\) : 9 \(x^2y^2z^2\) = 3y\(z^2\)
5. \(\left(-x\right)^{10}:\left(-x\right)^5=\left(-x\right)^2\) = x
1: \(\Leftrightarrow3x+4x=4\)
=>7x=4
hay x=4/7
2: \(\Leftrightarrow3x-5x-5^3:5^2=0\)
=>-2x=5
=>x=-5/2
1: \(=\dfrac{x^2-1}{x\left(x^2-1\right)}=\dfrac{1}{x}\)
2: \(=\dfrac{\left(x-2\right)\left(x+2\right)}{y\left(x-2\right)}=\dfrac{x+2}{y}\)
3: \(=\dfrac{2x^2+2xy-xy-y^2}{\left(x-y\right)\left(x+y\right)}=\dfrac{\left(x+y\right)\left(2x-y\right)}{\left(x-y\right)\left(x+y\right)}=\dfrac{2x-y}{x-y}\)
4: \(=\dfrac{x\left(x^2-1\right)}{x\left(x^2-x-2\right)}=\dfrac{\left(x-1\right)\left(x+1\right)}{\left(x-2\right)\left(x+1\right)}=\dfrac{x-1}{x-2}\)
A=26x2+y(2x+y)-10x(x+y)
A=26x2+2xy+y2-10x2-10xy
A=16x2-8xy+y2 =(4x)2-2.4x.y+y2 =(4x-y)2
Thay x=0,25y,ta có: A=(4.0,25y - y)2=(y-y)2=0
B=x3+6x2y+12xy2+8y3
B=x3+3x22y+3x(2y)2+(2y)3 =(x+2y)3
Có x+2y=-5 ⇒ x=-5-2y
Thay x=-5-2y vào, ta có B=(-5-2y+2y)3=(-5)3=-125
a) 25x² - 10xy + y²
= (5x)² - 2.5x.y + y²
= (5x - y)²
b) 4/9 x² + 20/3 xy + + 25y²
= (2/3 x)² + 2.2/3 x.5y + (5y)²
= (2/3 x + 5y)²
c) 9x² - 12x + 4
= (3x)² - 2.3x.2 + 2²
= (3x - 2)²
d) Sửa đề: 16u²v⁴ - 8uv² + 1
= (4uv²)² - 2.4uv².1 + 1²
= (4uv² - 1)²
1,\(\dfrac{x^2-6x+9}{x^2-8x+15}=\dfrac{\left(x-3\right)^2}{\left(x-3\right).\left(x-5\right)}=\dfrac{x-3}{x-5}\)
2,\(\dfrac{x^2+5x}{2x+10}=\dfrac{x.\left(x+5\right)}{2.\left(x+5\right)}=\dfrac{x}{2}\)
3,\(\dfrac{25-10x+x^2}{xy-5y}=\dfrac{\left(x-5\right)^2}{y.\left(x-5\right)}=\dfrac{x-5}{y}\)
4,\(\dfrac{x^2+3x-y^2-3y}{x^2-y^2}\\ \\ =\dfrac{\left(x+y\right).\left(x-y\right)+3.\left(x-y\right)}{\left(x-y\right).\left(x+y\right)}\\ \\ =\dfrac{\left(x-y\right).\left(x+y+3\right)}{\left(x-y\right).\left(x+y\right)}\\ \\ =\dfrac{x+y+3}{x+y}\)5,\(\dfrac{x^3+2x^2-x-2}{x^3-3x+2}=\dfrac{x^2.\left(x+2\right)-\left(x+2\right)}{x.\left(x^2-1\right)-2.\left(x-1\right)}\\ \\ \dfrac{\left(x+2\right).\left(x^2-1\right)}{x.\left(x+1\right).\left(x-1\right)-2.\left(x-1\right)}\\ =\dfrac{\left(x+2\right).\left(x+1\right).\left(x-1\right)}{\left(x-1\right).\left[\left(x+1\right).x-2\right]}=\dfrac{\left(x+2\right).\left(x+1\right)}{\left(x+1\right).x-2}\)
\(25x^2-10xy+y^2=\left(5x\right)^2-2.5x.y+y^2=\left(5x-y\right)^2\)
\(\dfrac{4}{9}x^2+\dfrac{20}{3}xy+25y^2=\left(\dfrac{2}{3}x\right)^2+2.\dfrac{2}{3}x.5y+\left(5y\right)^2=\left(\dfrac{2}{3}x+5y\right)^2\)
1.x2-3=x2-(√3)2=(x-√3)(x+√3)
2.\(5x^2-7y^2=\left(\sqrt{5}x\right)^2-\left(\sqrt{7}x\right)^2=\left(\sqrt{5}x-\sqrt{7}x\right)\left(\sqrt{5}x+\sqrt{7}x\right)\)
3.x2-2xy+y2-z2+2zt-t2=(x2-2xy+y2)-(z2-2zt+t2)
=(x-y)2-(z-t)2=(x-y-z+t)(x-y+z-t)
4. x3-3x2+3x-1-y3 =(x3-3x2.1+3x.12-13)-y3=(x-1)3-y3
=(x-1-y)[(x-1)2+(x-1)y+y2]
=(x-y-1)(x2-2x+1+xy-y+y2)
a: \(=\dfrac{5x^2y^4}{-10x^2y}=-\dfrac{1}{2}y^3=-\dfrac{1}{2}\cdot8=-4\)
b: \(=\dfrac{15x^4y^2}{5x^3y}+\dfrac{20x^3y^2}{5x^2y}=3xy+4xy=7xy\)
\(=7\cdot\dfrac{1}{7}\cdot2009=2009\)