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a: \(=25x^2-4y^2+4y-1\)
\(=25x^2-\left(2y-1\right)^2\)
\(=\left(5x-2y+1\right)\left(5x+2y-1\right)\)
a, \(\left(5x-2y\right)\left(5x+2y\right)+4y-1=25x^2-4y^2+4y-1\)
\(=\left(5x\right)^2-\left(4y^2-4y+1\right)=\left(5x\right)^2-\left(2y-1\right)^2=\left(5x-2y+1\right)\left(5x+2y-1\right)\)
b, t đag loading :)) phải vận dụng kiến thức đầu có nhóm zô, tí giải choa nhá :)
a) 5x2 ( 3x2 -7x+2)-15x(x-3)
=15x4-35x3+10x2-15x2+45x
=15x4-35x3-5x2+45x
c) (x+3)(x-3)(x-2)(x+1)
=(x2-9)(x2+x-2x-2)
=(x2-9)(x2-x-2)
=x4-x3-2x2-9x2+9x+18
=x4-x3-11x2+9x+18
d)(2x+1)2+(4x-1)2+2(2x+1)(4x+1)
=2x2+4x+1-16x2-8x+1
=2x2+4x+1-16x2-8x+1+16x2-4x+8x-2
=2x2+7
e) (2x2-3x)(5x2-2x+1)-10x2(x+3)
=10x4 -4x3+2x2-15x3+6x2-3 -10x2-30x
=10x4-19x3-2x2-30x-3
\(\frac{1}{x-5x^2}\)\(-\)\(\frac{25x-15}{25x^2-1}\)\(=\)\(\frac{-1}{x\left(5x-1\right)}\)\(-\)\(\frac{25x-15}{\left(5x-1\right)\left(5x+1\right)}\)
\(=\)\(\frac{-1\left(5x+1\right)}{x\left(5x-1\right)\left(5x+1\right)}\)\(-\)\(\frac{\left(25x^{ }-15\right)x}{\left(5x-1\right)\left(5x+1\right)x}\)
\(=\) \(\frac{-5x-1-25x^2+15x}{x\left(5x-1\right)\left(5x+1\right)}\)\(=\)\(\frac{-25x^2+10x-1}{x\left(5x-1\right)\left(5x+1\right)}\)
\(=\)\(\frac{-\left(5x-1\right)^2}{x\left(5x-1\right)\left(5x+1\right)}\)\(=\)\(\frac{-5x+1}{5x^2+x}\)
\(\frac{1}{x-5x^2}-\frac{25x-15}{25x^2-1}\)
\(=\frac{1}{x\left(1-5x\right)}-\frac{25x-15}{\left(5x-1\right)\left(5x+1\right)}\)
\(=\frac{1}{x\left(1-5x\right)}+\frac{25x-15}{\left(1-5x\right)\left(5x+1\right)}\)
\(=\frac{5x+1}{x\left(1-5x\right)\left(5x+1\right)}+\frac{\left(25x-15\right)x}{x\left(1-5x\right)\left(5x+1\right)}\)
\(=\frac{5x+1+25x^2+15x}{x\left(1-5x\right)\left(5x-1\right)}\)
\(=\frac{25x^2-10x+1}{x\left(1-5x\right)\left(5x+1\right)}\)
\(=\frac{\left(5x-1\right)^2}{x\left(1-5x\right)\left(5x+1\right)}\)
\(=\frac{\left(1-5x\right)^2}{x\left(1-5x\right)\left(5x+1\right)}\)
\(=\frac{1-5x}{x\left(5x+1\right)}\)
a,\(\frac{1}{5}x^2y\left(15xy^2-5y+3xy\right)=3x^3y^3-x^2y^2+\frac{3}{5}x^3y^2\)
b,\(5x^3-5x=5x\left(x^2-1\right)=5x\left(x-1\right)\left(x+1\right)\)
c, \(3x^2+5y-3xy-5x=3x\left(x-y\right)-5\left(x-y\right)\)
\(=\left(3x-5\right)\left(x-y\right)\)
1) 1/5x2y( 15xy2 - 5y + 3xy ) = 3x3y3 - x2y2 + 3/5x3y2
2) a) 5x3 - 5x = 5x( x2 - 1 ) = 5x( x2 - 12 ) = 5x( x - 1 )( x + 1 )
b) 3x2 + 5y - 3xy - 5x = ( 3x2 - 3xy ) + ( 5y - 5x )
= 3x( x - y ) + 5( y - x )
= 3x( x - y ) + 5[ -( x - y ) ]
= 3x( x - y ) - 5( x - y )
= ( 3x - 5 )( x - y )
\(5x^3-5x=5x\left(x^2-1\right)\)
\(3x^2+5x-3xy-5x=x\left(3x+5\right)-x\left(3y+5\right)=x\left(3x-3y\right)=3x\left(x-y\right)\)
Ta có: 1(x−2)2−1x+2−14−x21(x−2)2−1x+2−14−x2
=x+2−(x−2)2+x−2(x−2)2⋅(x+2)=x+2−(x−2)2+x−2(x−2)2⋅(x+2)
=2x−x2+4x−4(x−2)2⋅(x+2)=2x−x2+4x−4(x−2)2⋅(x+2)