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YI
3
20 tháng 9 2020
1) \(a^6-b^6=\left(a^2-b^2\right)\left(a^4+a^2b^2+b^4\right)=\left(a-b\right)\left(a+b\right)\left(a^4+a^2b^2+b^4\right)\)
2) \(27x^3-a^3b^3=\left(3x-ab\right)\left(9x^2+3xab+a^2b^2\right)\)
3) \(\frac{1}{8}-8x^3=\left(\frac{1}{2}-2x\right)\left(\frac{1}{4}+x+4x^2\right)\)
4) \(8+\left(4x-3\right)^3=\left(2+4x-3\right)\left[4-2\left(4x-3\right)+\left(4x-3\right)^2\right]\)
\(=\left(4x-1\right)\left(4-8x+6+16x^2-24x+9\right)\)
\(=\left(4x-1\right)\left(16x^2-32x+19\right)\)
PA
16 tháng 10 2016
\(2x^2+3x-27=2x^2-6x+9x-27=2x\left(x-3\right)+9\left(x-3\right)=\left(2x+9\right)\left(x-3\right)\)
\(x^3-7x+6=x^3-x-6x+6=x\left(x^2-1\right)-6\left(x-1\right)=x\left(x-1\right)\left(x+1\right)-6\left(x-1\right)=\left(x-1\right)\left(x^2+x-6\right)\)
\(x^3+5x^2+8x+4=x^3+x^2+4x^2+8x+4=x^2\left(x+1\right)+4\left(x^2+2x+1\right)=x^2\left(x+1\right)+4\left(x+1\right)^2\)
\(=\left(x+1\right)\left(x^2+4x+4\right)=\left(x+1\right)\left(x+2\right)^2\)
\(27x^3-27x^2+18x-4=27x^3-9x^2-18x^2+6x+12x-4\)
\(=9x^2\left(3x-1\right)-6x\left(3x-1\right)+4\left(3x-1\right)=\left(3x-1\right)\left(9x^2-6x+4\right)\)
HP
15 tháng 10 2020
e, \(x^3+5x^2+8x+4=x^3+x^2+4x^2+4x+4x+4\)
\(=x^2\left(x+1\right)+4x\left(x+1\right)+4\left(x+1\right)\)
\(=\left(x+1\right)\left(x^2+4x+4\right)=\left(x+1\right)\left(x+2\right)^2\)
d, \(27x^3-27x^2+18x-4=27x^3-9x^2-18x^2+6x+12x-4\)
\(=9x^2\left(3x-1\right)-6x\left(3x-1\right)+4\left(3x-1\right)\)
\(=\left(3x-1\right)\left(9x^2-6x+4\right)\)
NN
2
16 tháng 7 2022
Bài 1:
\(B=\dfrac{1}{9}x^2-2x+9\)
\(=\left(\dfrac{1}{3}x\right)^2-2\cdot\dfrac{1}{3}x\cdot3+3^2=\left(\dfrac{1}{2}x-3\right)^2\)
\(C=x^3-9x^2+27x-27=\left(x-3\right)^3\)
\(D=27x^3+27x^2+9x+1=\left(3x+1\right)^3\)
\(E=\left(x-2y\right)^3\)
21 tháng 7 2019
a) \(27x^3+8^3\)
\(=\left(3x\right)^3+2^3\)
\(=\left(3x+2\right)\left[\left(3x\right)^2+6x+2^2\right]\)
\(=\left(3x+2\right)\left(9x^2-6x+4\right)\)
b) \(8x^3-y^3\)
\(=\left(2x-y\right)\left(4x^2+2xy+y^2\right)\)
c) \(x^2+4xy+4y^2\)
\(=\left(x+2y\right)^2\)
21 tháng 7 2019
\(27x^3+8\)
\(=\left(3x\right)^3+2^3\)
\(=\left(3x+2\right)\left(9x^2-6x+4\right)\)
\(8x^3-y^3\)
\(=\left(2x\right)^3-y^3\)
\(=\left(2x-y\right)\left(4x^2+2xy+y^2\right)\)
\(x^2+4xy+4y^2\)
\(=x^2+2.x.2y+\left(2y\right)^2\)
\(=\left(x+2y\right)^2\)
_Minh ngụy_
a) 216x3 + ( x + y )3 = ( 6x )3 + ( x + y )3
= [ 6x + ( x + y ) ][ ( 6x )2 - 6x( x + y ) + ( x + y )2 ]
= ( 6x + x + y )( 36x2 - 6x2 - 6xy + x2 + 2xy + y2 )
= ( 7x + y )( 31x2 - 4xy + y2 )
b) ( 2x + 1 )3 + 8x3 = ( 2x + 1 )2 + ( 2x )3
= [ ( 2x + 1 ) + 2x ][ ( 2x + 1 )2 - ( 2x + 1 )2x + ( 2x )2
= ( 2x + 1 + 2x )( 4x2 + 4x + 1 - 4x2 - 2x + 4x2 )
= ( 4x + 1 )( 4x2 + 2x + 1 )
c) ( 5x - 2 )3 - 27x3 = ( 5x - 2 ) - ( 3x )3
= [ ( 5x - 2 ) - 3x ][ ( 5x - 2 )2 + ( 5x - 2 )3x + ( 3x )2
= ( 5x - 2 - 3x )( 25x2 - 20x + 4 + 15x2 - 6x + 9x2 )
= ( 2x - 2 )( 49x2 - 26x + 4 )
= 2( x - 1 )( 49x2 - 26x + 4 )
a) \(216x^3+\left(x+y\right)^3=\left(6x\right)^3+\left(x+y\right)^3\)
\(=\left(6x+x+y\right)\left[\left(6x\right)^2-6x\left(x+y\right)+\left(x+y\right)^2\right]\)
\(=\left(7x+y\right)\left(36x^2-6x^2-6xy+x^2+2xy+y^2\right)\)
\(=\left(7x+y\right)\left(31x^2-4xy+y^2\right)\)
b) \(\left(2x+1\right)^3+8x^3=\left(2x+1\right)^3+\left(2x\right)^3\)
\(=\left(2x+1+2x\right)\left[\left(2x+1\right)^2-2x\left(2x+1\right)+\left(2x\right)^2\right]\)
\(=\left(4x+1\right)\left(4x^2+4x+1-\left(4x^2-2x\right)+4x^2\right)\)
\(=\left(4x+1\right)\left(4x^2+1+2x\right)\)
c) \(\left(5x-2\right)^3-27x^3=\left(5x-2\right)^3-\left(3x\right)^3\)
\(=\left(5x-2-3x\right)\left[\left(5x-2\right)^2+3x\left(5x-2\right)+\left(3x\right)^2\right]\)
\(=\left(2x-2\right)\left(25x^2-20x+4+15x^2-6x+9x^2\right)\)
\(=\left(2x-2\right)\left(49x^2-26x+4\right)\)