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a) x2 + 6x + 9 = x2 + 2 . x . 3 + 32 = (x + 3)2
b) 10x – 25 – x2 = -(-10x + 25 +x2) = -(25 – 10x + x2)
= -(52 – 2 . 5 . x – x2) = -(5 – x)2
c) 8x3 - 1/8 = (2x)3 – (1/2)3 = (2x - 1/2)[(2x)2 + 2x . 12 + (1/2)2]
= (2x - 1/2)(4x2 + x + 1/4)
d)1/25x2 – 64y2 = (1/5x)2(1/5x)2- (8y)2 = (1/5x + 8y)(1/5x - 8y)
a) \(3x\left(x+1\right)^2-5x^2\left(x+1\right)+7\left(x+1\right)\)
\(=\left(x+1\right)\left[3x\left(x+1\right)-5x^2+7\right]\)
\(=\left(x+1\right)\left(3x^2+3x-5x^2+7\right)\)
\(=\left(x+1\right)\left(-2x^2+3x+7\right)\)
\(=-\left(x+1\right)\left(2x^2-3x-7\right)\)
b) \(\left(x+y\right)\left(2x-y\right)-\left(3x-y\right)\left(y-2x\right)\)
\(=\left(x+y\right)\left(2x-y\right)+\left(3x-y\right)\left(2x-y\right)\)
\(=\left(2x-y\right)\left(x+y+3x-y\right)\)
\(=4x\left(2x-y\right)\)
c) \(5u\left(u-v\right)^2+10u^2\left(v-u\right)^2\)
\(=5u\left(u-v\right)^2+10u^2\left(u-v\right)^2\)
\(=5u\left(u-v\right)^2\left(1+2u\right)\)
Trả lời:
a, 3x ( x + 1 )2 - 5x2 ( x + 1 ) + 7 ( x + 1 )
= ( x + 1 )[ 3x ( x + 1 ) - 5x2 + 7 ]
= ( x + 1 )( 3x2 + 3x - 5x2 + 7 )
= ( x + 1 )( - 2x2 + 3x + 7 )
b, ( x + y )( 2x - y ) - ( 3x - y )( y - 2x )
= ( x + y )( 2x - y ) + ( 3x - y )( 2x - y )
= ( 2x - y )( x + y + 3x - y )
= 4x ( 2x - y )
c, 5u ( u - v )2 + 10u2 ( v - u )2
= 5u ( u - v )2 + 10u2 ( u - v )2
= 5u ( u - v )2( 1 + 2u )
a) 5x2 - 5xy - 3x + 3y
= 5x.(x - y) - 3.(x - y)
= (x - y).(5x - 3)
b) x3 - 2x2 - x + 2
= x2.(x - 2) - (x - 2)
= (x - 2).(x2 - 1)
= (x - 2).(x - 1).(x + 1)
a/ 5x2-5xy-3x+3y
=5x.(x-y)-3(x-y)
=(5x-3).(x-y)
b/ x3-2x2-x+2
=x2.(x-2)-(x-2)
=(x2-1).(x-2)
=(x-1).(x+1).(x-2)
Ta có: x2y+5xy-14y
= y(x2+5x-14)
= y(x+7)(x-2)
x3-5x2-14x
= x(x2-5x-14)
= x(x-7)(x+2)
\(x^2y+5xy-14y\)
\(=x^2y-2xy+7xy-14y\)
\(=xy\left(x-2\right)+7y\left(x-2\right)\)
\(=\left(x-2\right)\left(xy+7y\right)\)
\(x^3-5x^2-14x\)
\(=x^3-7x^2+2x^2-14x\)
\(=x^2\left(x-7\right)+2x\left(x-7\right)\)
\(=\left(x^2+2x\right)\left(x-7\right)\)
\(=x\left(x+2\right)\left(x-7\right)\)
a,\(x^2y-4y=y\left(x^2-4\right)=y\left(x-2\right)\left(x+2\right)\)
b,\(x^2-y^2-2x+1=\left(x^2-2x+1\right)-y^2\)
\(=\left(x-1\right)^2-y^2\)
\(=\left(x-y+1\right)\left(x-y-1\right)\)
c,\(5x^2+5xy-x-y=5x\left(x+y\right)-\left(x+y\right)\)
\(=\left(5x-1\right)\left(x+y\right)\)
x2y - 4y = y( x2 - 4 ) = y( x - 2 )( x + 2 )
x2 - y2 - 2x + 1 = ( x2 - 2x + 1 ) - y2 = ( x - 1 )2 - y2 = ( x - 1 - y )( x - 1 + y )
5x2 + 5xy - x - y = ( 5x2 + 5xy ) - ( x + y ) = 5x( x + y ) - ( x + y ) = ( x + y )( 5x - 1 )
\(5x^3-5xy^2+10xy-5x\)
\(=5x\left(x^2-y^2+2y-1\right)\)
\(=5x\left[x^2-y^2+y+y-1\right]\)
\(=5x\left[x^2-y\left(y-1\right)+\left(y-1\right)\right]\)
\(=5x\left[x^2-\left(y+1\right)\left(y-1\right)\right]\)
\(=5x\left[x^2-\left(y^2-1^2\right)\right]\)
\(=5x\left[\left(x-y\right)\left(x+y\right)+1\right]\)
Lâu k làm, sai thông cảm
\(a.=x^3-2x^2+x^2-2x+x-2=x^2\left(x-2\right)+x\left(x-2\right)+\left(x-2\right)=\left(x-2\right)\left(x^2+x+2\right)\)
b.\(=2x^3+x^2-2x^2-x-2x-1=x^2\left(2x+1\right)-x\left(2x-1\right)-\left(2x-1\right)\)\(=\left(2x-1\right)\left(x^2-x-1\right)\)
c.\(3x^3-x^2+6x^2-2x-12x+4=x^2\left(3x-1\right)+2x\left(3x-1\right)-4\left(3x-1\right)\)\(=\left(3x-1\right)\left(x^2+2x-4\right)\)
d.\(3x^3-x^2-6x^2+2x+15x-5=x^2\left(3x-1\right)-2x\left(3x-1\right)+5\left(3x-1\right)\)\(=\left(3x-1\right)\left(x^2-2x+5\right)\)
t i c k cho mình nha
`Answer:`
`(3x+1)^2 -(x+1)`
`=(3x)^2 +2.3x.1+1^2 -x-1`
`=9x^2 +6x+1-x-1`
`=9x^2 +(6x-x)+(1-1)`
`=9x^2 +5x`
`5x^2+5xy-x-y`
`=(5x^2+5xy)-(x+y)`
`=5x.(x+y)-(x+y)`
`=(5x-1)(x+y)`