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a) \(x^3+6x^2+12x+8\)
\(=\left(x+2\right)^3\)
b) \(x^3-3x^2+3x-1\)
\(=\left(x-1\right)^3\)
c) \(1-9x+27x^2-27x^3\)
\(=-\left(27x^3-27x^2+9x-1\right)\)
\(=-\left(3x-1\right)^3\)
a) 3x2 - 7x + 2
= 3x2 - 6x - x + 2
= (3x2 - 6x) - (x - 2)
= 3x (x - 2) - (x - 2)
= (3x - 1) (x - 2)
a, 4x2 - 12x + 9
= (2x + 3)2
b, 9x4y3 + 3x2y4
= 3x2y3(3x2 + y)
c, ( x - 3 )2 - 2x ( x - 3 )
= (x - 3)(x - 3 - 2x)
= (x - 3)(-x - 3)
d, 3x ( x - 1 ) + 6 ( x - 1 )
= 3(x - 1)(x + 2)
e, 2x ( x + 1 ) - 4x - 4
= 2x(x + 1) - 4(x + 1)
= (x + 1)(2x - 4)
= 2(x + 1)(x - 2)
f, ( 2x - 3 )2 - 4x + 6
= (2x - 3)2 - 2(2x - 3)
= (2x - 3)(2x - 3 - 2)
= (2x - 3)(2x - 5)
a,\(xy+3x-7y-21\)
\(=x\left(y+3\right)-7\left(y+3\right)\)
\(=\left(y+3\right)\left(x-7\right)\)
\(b,2xy-15-6x+5y\)
\(=\left(2xy-6x\right)+\left(-15+5y\right)\)
\(=2x\left(y-3\right)-5\left(3-y\right)\)
\(=2x\left(y-3\right)+5\left(y-3\right)\)
\(=\left(y-3\right)\left(2x+5\right)\)
\(x^2-y^2+4x+4\)
\(=\left(x+2\right)^2-y^2\)
\(=\left(x+2+y\right)\left(x+2-y\right)\)
\(4x^2-y^2+8\left(y-2\right)\)
\(=4x^2-\left(y^2-8y+16\right)\)
\(=4x^2-\left(y-4\right)^2\)
\(=\left(2x+y-4\right)\left(2x-y+4\right)\)
a,X^3-16x =x(x^2-16)
b,y(y-2)-3(y-2)=(y+3).(y-2)
c,x^2+4x+4-y^2=(x+2)^2-y^2=(x+y+2).(x+2-Y)
D,4^2y^3-12x^2y^4+16X^5y^3=4x^2y^2(y-3y^2+4X^3y)
a) \(=2xy^2\left(x^2+8x+15\right)\)
\(=2xy^2\left[\left(x^2+8x+16\right)-1\right]\)
\(=2xy^2\left[\left(x+4\right)^2-1\right]\)
\(=2xy^2\left(x+4+1\right)\left(x+4-1\right)\)
\(=2xy^2\left(x+5\right)\left(x-3\right)\)
mấy câu sau tự làm nha :*
b,=(x^2-10x+25)-4
=(x-5)^2-2^2
=(x-5-2)(x-5+2)
=(x-7)(x-3)
a) 5x3 - 40 = 5( x3 - 8 ) = 5( x - 2 )( x2 + 2x + 4 )
b) x2z + 4xyz + 4y2z = z( x2 + 4xy + 4y2 ) = z( x + 2y )2
c) 4x2 - y2 - 6x + 3y = ( 4x2 - y2 ) - ( 6x - 3y ) = ( 2x - y )( 2x + y ) - 3( 2x - y ) = ( 2x - y )( 2x + y - 3 )
d) x2 + 2x - 4y2 + 1 = ( x2 + 2x + 1 ) - 4y2 = ( x + 1 )2 - ( 2y )2 = ( x - 2y + 1 )( x + 2y + 1 )
e) 3x2 - 3y2 - 12x + 12y = 3( x2 - y2 - 4x + 4y ) = 3[ ( x2 - y2 ) - ( 4x - 4y ) ] = 3[ ( x - y )( x + y ) - 4( x - y ) ] = 3( x - y )( x + y - 4 )
f) x3 + 5x2 + 4x + 20 = x2( x + 5 ) + 4( x + 5 ) = ( x + 5 )( x2 + 4 )
g) x3 - x2 - 25x + 25 = x2( x - 1 ) - 25( x - 1 ) = ( x - 1 )( x2 - 25 ) = ( x - 1 )( x - 5 )( x + 5 )
a) \(5x^3-40=5\left(x^3-8\right)=5\left(x-2\right)\left(x^2+2x+4\right)\)
b) \(x^2z+4xyz+4y^2z=z\left(x^2+4xy+4y^2\right)=z\left(x+2y\right)^2\)
c) \(4x^2-y^2-6x+3y=\left(4x^2-y^2\right)-\left(6x-3y\right)\)
\(=\left(2x-y\right)\left(2x+y\right)-3\left(2x-y\right)=\left(2x-y\right)\left(2x+y-3\right)\)
d) \(x^2+2x-4y^2+1=x^2+2x+1-4y^2\)
\(=\left(x+1\right)^2-4y^2=\left(x+2y+1\right)\left(x-2y+1\right)\)
e) \(3x^2-3y^2-12x+12y=3\left(x^2-y^2-4x+4y\right)\)
\(=3\left[\left(x^2-y^2\right)-\left(4x-4y\right)\right]=3\left[\left(x-y\right)\left(x+y\right)-4\left(x-y\right)\right]\)
\(=3\left(x-y\right)\left(x+y+4\right)\)
f) \(x^3+5x^2+4x+20=\left(x^3+5x^2\right)+\left(4x+20\right)\)
\(=x^2.\left(x+5\right)+4\left(x+5\right)=\left(x^2+4\right)\left(x+5\right)\)
g) \(x^3-x^2-25x+25=\left(x^3-x^2\right)-\left(25x-25\right)\)
\(=x^2\left(x-1\right)-25\left(x-1\right)=\left(x-1\right)\left(x^2-25\right)\)
\(=\left(x-1\right)\left(x-5\right)\left(x+5\right)\)
các bạn ơi giúp mk với
a) 3x^3 - 75x
a^2 - b^2= (a+b)(a-c) trong đó a=x và b=5
3x(x+5)(x-5)
b) 5x^2y^2 -30xy + 45y^3
= 5y(x^2y-6x+9y^2)
c) 4x^3 - 500
= a^3 - b^3 = (a-b)(a^2+ab+b^2) trong đó a = x và b=5
=> 4(x-5)(x^2+5x+25)
a) \(3x^3-75x=3x\left(x^2-25\right)=3x\left(x-5\right)\left(x+5\right)\)
b) \(5x^2y^2-30xy+45y^3\)
\(=5\left(x^2y^2-6xy+9y^3\right)\)
c) \(4x^3-500=4\left(x^3-125\right)=4\left(x-5\right)\left(x^2+5x+25\right)\)
d) \(x^4y^2-12x^3y^2+48x^2y^2-64xy^2\)
\(=xy^2\left(x^3-12x^2+48x-64\right)\)
\(=xy^2\left(x-4\right)^3\)
e) \(x^4-4x^2-4x-1\)
\(=x^4-\left(2x+1\right)^2\)
\(=\left(x^2-2x-1\right)\left(x^2-2x+1\right)\)
\(=\left(x-2x-1\right)\left(x-1\right)^2\)
g) \(x^4+6x^3-54x-81\)
\(=\left(x^4+3x^3\right)+\left(3x^3+9x^2\right)-\left(9x^2+27x\right)-\left(27x+81\right)\)
\(=\left(x+3\right)\left(x^3+3x^2-9x-27\right)\)
\(=\left(x+3\right)\left[x^2\left(x+3\right)-9\left(x+3\right)\right]\)
\(=\left(x+3\right)^3\left(x-3\right)\)
d) x4y2 - 12x3y2 +48x2y2
=x2y2(x2-12x+48)
a) 3x3 - 75x
= 3x( x2 - 25 )
= 3x( x - 5 )( x + 5 )
b) 5x2y2 - 30xy + 45y3
= 5y( x2y - 6x + 9y2 )
c) 4x3 - 500
= 4( x3 - 125 )
= 4( x - 5 )( x2 + 5x + 25 )
d) x4y2 - 12x3y2 + 48x2y2 - 64xy2
= xy2( x3 - 12x2 + 48x - 64 )
= xy2( x - 4 )3
e) x4 - 4x2 - 4x - 1
= x4 - 2x3 + 2x3 - x2 - 4x2 + x2 - 2x - 2x - 1
= ( x4 - 2x3 - x2 ) + ( 2x3 - 4x2 - 2x ) + ( x2 - 2x - 1 )
= x2( x2 - 2x - 1 ) + 2x( x2 - 2x - 1 ) + 1( x2 - 2x - 1 )
= ( x2 - 2x - 1 )( x2 + 2x + 1 )
= ( x2 - 2x - 1 )( x + 1 )2
g) x4 + 6x3 - 54x - 81
= x4 + 9x3 - 3x3 + 27x2 - 27x2 + 27x - 81x - 81
= ( x4 + 9x3 + 27x2 + 27x ) - ( 3x3 + 27x2 + 81x + 81 )
= x( x3 + 9x2 + 27x + 27 ) - 3( x3 + 9x2 + 27x + 27 )
= ( x3 + 9x2 + 27x + 27 )( x - 3 )
= ( x + 3 )3( x - 3 )
a,\(3x^3-75x\)
\(=3x\left(x^2-25\right)\)
\(=3x\left(x-5\right)\left(x+5\right)\)
b,\(5x^2y^2-30xy+45y^3\)
\(=5y\left(x^2y-6x+9y^2\right)\)
c,\(4x^3-500\)
\(=4\left(x^3-125\right)\)
\(=4\left(x^3-5^3\right)\)
\(=4\left[\left(x-5\right)\left(x^2+5x+25\right)\right]\)
\(=4\left(x-5\right)\left(x^2+5x+25\right)\)
d,\(x^4y^2-12x^3y^2+48x^2y^2-64xy^2\)
\(=xy^2\left(x^3-12x^2+48x-64\right)\)
\(=xy^2\left(x-4\right)^3\)
Bài làm :
a) 3x3 - 75x
= 3x( x2 - 25 )
= 3x( x - 5 )( x + 5 )
b) 5x2y2 - 30xy + 45y3
= 5y( x2y - 6x + 9y2 )
c) 4x3 - 500
= 4( x3 - 125 )
= 4( x - 5 )( x2 + 5x + 25 )
d) x4y2 - 12x3y2 + 48x2y2 - 64xy2
= xy2( x3 - 12x2 + 48x - 64 )
= xy2( x - 4 )3
e) x4 - 4x2 - 4x - 1
= x4 - 2x3 + 2x3 - x2 - 4x2 + x2 - 2x - 2x - 1
= ( x4 - 2x3 - x2 ) + ( 2x3 - 4x2 - 2x ) + ( x2 - 2x - 1 )
= x2( x2 - 2x - 1 ) + 2x( x2 - 2x - 1 ) + 1( x2 - 2x - 1 )
= ( x2 - 2x - 1 )( x2 + 2x + 1 )
= ( x2 - 2x - 1 )( x + 1 )2
g) x4 + 6x3 - 54x - 81
= x4 + 9x3 - 3x3 + 27x2 - 27x2 + 27x - 81x - 81
= ( x4 + 9x3 + 27x2 + 27x ) - ( 3x3 + 27x2 + 81x + 81 )
= x( x3 + 9x2 + 27x + 27 ) - 3( x3 + 9x2 + 27x + 27 )
= ( x3 + 9x2 + 27x + 27 )( x - 3 )
= ( x + 3 )3( x - 3 )