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a) \(2x^2\left(3x-5\right)=2x^2.3x-2x^2.5=6x^3-10x^2\)
b) \(\left(12x^3y+18x^2y\right):2xy\)\(=12x^3y:2xy+18x^2y:2xy\)
\(=6x^2+9x=3x\left(2x+3\right)\)
1. Ta có : 2x4 - 3x3 - 3x2 + 6x - 2
= 2x4 - 2x3 - x3 + x2 - 4x2 + 4x + 2x - 2
= 2x3( x - 1 ) - x2( x - 1 ) - 4x( x - 1 ) + 2( x - 1 )
= ( x - 1 )( 2x3 - x2 - 4x + 2 )
= ( x - 1 )[ x2( 2x - 1 ) - 2( 2x - 1 ) ]
= ( x - 1 )( 2x - 1 )( x2 - 2 )
=> ( 2x4 - 3x3 - 3x2 + 6x - 2 ) : ( x2 - 2 ) = ( x - 1 )( 2x - 1 ) = 2x2 - 3x + 1
2. \(\left(15x^4y^6-12x^3y^4-18x^2y^3\right)\div\left(-6x^2y^2\right)\)
\(=\frac{15x^4y^6}{-6x^2y^2}-\frac{12x^3y^4}{-6x^2y^2}-\frac{18x^2y^3}{-6x^2y^2}\)
\(=-\frac{5}{2}x^2y^4+2xy^2+3y\)
\(x\left(2-3x\right)+\left(3x^2-x^2\right):x\)
\(=2x-3x^2+3x^2-x\)
\(=x\)
\(2x\left(x-3y\right)-\left(8x^3y-12x^2y^2\right):2xy\)
\(=2x^2-6xy-4x^2+6xy\)
\(=-2x^2\)
Thực hiện phép tính:
a. ( 2x - 6 )( 12x2 + 9x + 36 )
b. ( 2x4 + x3 - 3x2 + 5x - 2 ) : ( 5x2 - 5x + 5 )
a ) \(\left(x+1\right)\left(x-2\right)=x^2-2x+x-2=x^2-x-2\)
b ) \(\left(4x^4y^4-12x^2y^2\right):4x^2y^2=x^2y^2-3\)
c ) \(\frac{3x^2-1}{2x}+\frac{x^2+1}{2x}=\frac{3x^2-1+x^2+1}{2x}=\frac{4x^2}{2x}=2x\)
d ) \(\frac{x^2}{x-1}+\frac{2x}{1-x}+\frac{1}{x-1}=\left(\frac{x^2}{x-1}+\frac{1}{x-1}\right)+\frac{2x}{1-x}\)
\(=\frac{x^2+1}{x-1}+\frac{2x}{1-x}=\frac{x^2+1}{x-1}+\frac{-2x}{x-1}=\frac{x^2+1-2x}{x-1}=\frac{\left(x-1\right)^2}{x-1}=x-1\)
a) .......=x2-x-2
b) .........=x2y2-3
c) .......=(3x2-1+x2+1)/2x=4x2/2x=2x
d) x2 /(x-1)+(-2x)/(x-1)+1/(x-1)=(x2-2x+1)/(x-1)=(x-1)2/(x-1)=x-1
e)...
x-y=4
=> x2-2xy+y2=16
<=> 106-2xy =16 (vì x2+y2 =106)
=>xy=(106-16)/2=45
ta có x3 -y3 =(x-y)(x2+xy+y2 )
=4(106+45)=604
Bài làm
a, \(2x^2\left(3x-5\right)=6x^3-10x^2\)
b, \(\left(12x^3y^2-18x^2y\right):2xy=\left(12x^3y^2:2xy\right)-\left(18x^2y:2xy\right)=6x^2y-9x\)