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xy - 5y + 2x - 10= (xy + 2x) - (5y + 10) = x.(y + 2) - 5.(y + 2)= (y + 2).(x - 5)
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25x2(y-1)-5x3(1-y)
=25x2(y-1)+5x3(y-1)
=5x2(y-1)(5+x)
xy+2x+5y+10
=(xy+2x)+(5y+10)
=x(y+2)+5(y+2)
=(y+2)(x+5)
1; \(25x^2\left(y-1\right)-5x^3\left(1-y\right)=25x^2\left(y-1\right)+5x^3\left(y-1\right)=5x^2\left(y-1\right)\left(5+x\right)\)
2; \(xy+2x+5y+10=x\left(y+2\right)+5\left(y+2\right)=\left(x+5\right)\left(y+2\right)\)
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1, 25x^2 ( y - 1) - 5x^3 ( 1-y)
= 25x^2 ( y - 1) + 5x^3 ( y - 1)
= 5x^2 ( y - 1)( 1 + x)
2, xy + 2x + 5y + 10
= x( y + 2) + 5( y + 2)
= ( x + 5)( y+2)
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a: \(=\dfrac{3x-x+6}{x\left(2x+6\right)}=\dfrac{1}{x}\)
b: \(=\dfrac{1}{x\left(y-x\right)}-\dfrac{1}{y\left(y-x\right)}\)
\(=\dfrac{y-x}{xy\left(y-x\right)}=\dfrac{1}{xy}\)
c: \(=\dfrac{\left(1-2x\right)\left(1+2x\right)}{x\left(x+4\right)}\cdot\dfrac{3x}{2\left(1-2x\right)}\)
\(=\dfrac{3\left(1+2x\right)}{2\left(x+4\right)}\)
d: \(=\dfrac{12x}{8x^3}\cdot\dfrac{15y^4}{5y^3}=\dfrac{3}{2x^2}\cdot3y=\dfrac{9y}{2x^2}\)
f: \(=\dfrac{\left(x-2\right)\left(x+2\right)}{3\left(x+4\right)}\cdot\dfrac{x+4}{2\left(x-2\right)}=\dfrac{x+2}{6}\)
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a)x2-5x
=x(x-5)
b)(x+y)2-16
=(x+y)2-42
=(x+y-4)(x+y+4)
c)xy-2x+5y-10
=(xy-2x)+(5y-10)
=x(y-2)+5(y-2)
=(y-2)(x+5)
\(=y\left(x-5\right)+2\left(x-5\right)\)
\(=\left(y+2\right)\left(x-5\right)\)