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c ) \(4x^2-12x-160\)
\(=4x^2-32x+20x-160\)
\(=4x\left(x-8\right)+20\left(x-8\right)\)
\(=4.x\left(x-8\right)+4.5\left(x-8\right)\)
\(=4\left(x+5\right)\left(x-8\right)\)
d ) \(5x^2y-10xy-15y\)
\(=y\left(5x^2-10x-15\right)\)
\(=y\left(5x^2-15x+5x-15\right)\)
\(=y\left[5x\left(x-3\right)+5\left(x-3\right)\right]\)
\(=y\left[5.x\left(x-3\right)+5\left(x-3\right)\right]\)
\(=y.\left[5.\left(x+1\right)\left(x-3\right)\right]\)
\(=5y.\left(x+1\right)\left(x-3\right)\)
a) 3 ( 4x +5y )
b) (x-y) (x+y+1)
d) (x3)2 - 82 = (x3- 8) (x3+8)
a, 12x+15y = 3(4x+5y)
b, x^2 - y^2 - x - y = (x - y)(x + y) - (x + y) = (x + y)(x - y - 1)
c, x^3 + 2x^2 + x = x(x^2 + 2x + 1) = x(x + 1)^2
d, x^6 - 64 = (x^3 - 8)(x^3 + 8) = (x - 2)(x^2 + 2x + 4)(x + 2)(x^2 - 2x + 4)
a)5x2y-10xy2
=5xy(x-2y)
b,:4x(2y-z)+7y(z-2y)
=4x(2y-z)-7y(2y-z)
=(2y-z)(4x-7y)
c,:y(x-z)+7(z-x)
=y(x-z)-7(x-z)
=(x-z)(y-7)
d)36-12x+x^2
=x2-2.x.6+62
=(x-6)2
e) (x-5)^2-16
=(x-5)2-42
=(x-5-4)(x-5+4)
=(x-9)(x-1)
f) 8x^3+1/27
=(2x)3+(1/3)3
=(2x+1/3)(4x2+2/3.x+1/9)
a) \(-5x-10xy-15y=-5\left(x+2xy+3y\right) \)
b) \(3a^2x-ba^2y+12a=a\left(3ax-bay+12\right) \)
c) \(2\left(x-y\right)-a\left(y-x\right)=\left(2+a\right)\left(x-y\right) \)
d) \(3a\left(x-y\right)-a^2\left(y-x\right)=\left(3a+a^2\right)\left(x-y\right) \)
a) x2 + 2x - 8 = x2 - 2x + 4x - 8 = x(x - 2) + 4(x - 2) = (x - 2)(x - 4)
b) x2 + 5x + 6 = x2 + 2x + 3x + 6 = x(x + 2) + 3(x + 2) = (x + 2)(x + 3)
c) 4x2 - 12x + 8 = 4x2 - 4x - 8x + 8 = 4x(x - 1) - 8(x - 1) = (x - 1)(4x - 8)
d) 3x2 + 8xy + 5y2 = 3x2 + 3xy + 5xy + 5y2 = 3x(x + y) + 5y(x + y) = (x + y)(3x + 5y)
a) x2 + 2x - 8 = x2 - 2x + 4x - 8 = x( x - 2 ) + 4( x - 2 ) = ( x - 2 )( x + 4 )
b) x2 + 5x + 6 = x2 + 2x + 3x + 6 = x( x + 2 ) + 3( x + 2 ) = ( x + 2 )( x + 3 )
c) 4x2 - 12x + 8 = 4( x2 - 3x + 2 ) = 4( x2 - x - 2x + 2 ) = 4[ x( x - 1 ) - 2( x - 1 ) ] = 4( x - 1 )( x - 2 )
d) 3x2 + 8xy + 5y2 = 3x2 + 3xy + 5xy + 5y2 = 3x( x + y ) + 5y( x + y ) = ( x + y )( 3x + 5y )
Đổi dấu – (4yx2 + yz2)(z – y2) = (4yx2 + yz2)( y2 – z), ta có thừa số
(y2 – z) chung:
C = (y2 – z)(2x2y – yz) – (4yx2 + yz2)(z – y2) + 6x2z(y2 – z)
= (y2 – z)(2x2y – yz) + (4yx2 + yz2)( y2 – z) + 6x2z(y2 – z)
= (y2 – z)[( 2x2y – yz ) + (4yx2 + yz2) + 6x2z]
= (y2 – z)[ 2x2y + 4yx2 + 6x2z]
= (y2 – z)[ 2xy2 + 4yx2 + 6x2z]
= (y2 – z)[ 2x2(y + 2y + 3z)]
= (y2 – z)[ 2x2(3y + 3z)]
= (y2 – z) 2x2 .3(y + z)
= 6x2(y2 – z)(y + z).
a) 7x2 - 4x
= x ( 7x - 4 )
b) 5x2 - 2x + 10 xy - 4y
= x ( 5x - 2 ) + 2y ( 5x - 2 )
= ( x + 2y ) ( 5x - 2 )
a, x2 + x - 6
= x2 + 3x - 2x - 6
= x(x + 3) - 2(x + 3)
= (x + 3)(x - 2)
b, x2 - 2x - 15
= x2 - 5x + 3x -15
= x(x - 5) + 3(x - 5)
= (x + 3)(x - 5)
c,4x2 - 12x - 160
= 4x2 - 32x + 20x - 160
= 4x(x - 8) + 20(x - 8)
= (4x + 20)(x - 8)
d, 5x2y - 10xy - 15y
= y(5x2 - 10x - 15)
= y(5x2 - 15x + 5x - 15)
= y(5x(x - 3) + 5(x - 3)
= y(5x + 5)(x - 3)