a)3x mũ 2 y -6x
b)x mũ 2-4
c)5x mũ 2 + 5xy - x mũ 2 -2xy- y mũ 2
d) 6x mũ 2 +5x -4
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a) ( 5x - y )( 25x2 + 5xy + y2 ) = ( 5x )3 - y3 = 125x3 - y3
b) ( x - 3 )( x2 + 3x + 9 ) - ( 54 + x3 ) = x3 - 33 - 54 - x3 = -27 - 54 = -81
c) ( 2x + y )( 4x2 - 2xy + y2 ) - ( 2x - y )( 4x2 + 2xy + y2 ) = ( 2x )3 + y3 - [ ( 2x )3 - y3 ]= 8x3 + y3 - 8x3 + y3 = 2y3
d) ( x + y )2 + ( x - y )2 + ( x + y )( x - y ) - 3x2 = x2 + 2xy + y2 + x2 - 2xy + y2 + x2 - y2 - 3x2 = y2
e) ( x - 3 )3 - ( x - 3 )( x2 + 3x + 9 ) + 6( x + 1 )2
= x3 - 9x2 + 27x - 27 - ( x3 - 33 ) + 6( x2 + 2x + 1 )
= x3 - 9x2 + 27x - 27 - x3 + 27 + 6x2 + 12x + 6
= -3x2 + 39x + 6
= -3( x2 - 13x - 2 )
f) ( x + y )( x2 - xy + y2 ) + ( x - y )( x2 + xy + y2 ) - 2x3
= x3 + y3 + x3 - y3 - 2x3
= 0
g) x2 + 2x( y + 1 ) + y2 + 2y + 1
= x2 + 2x( y + 1 ) + ( y2 + 2y + 1 )
= x2 + 2x( y + 1 ) + ( y + 1 )2
= ( x + y + 1 )2
= [ ( x + y ) + 1 ]2
= ( x + y )2 + 2( x + y ) + 1
= x2 + 2xy + y2 + 2x + 2y + 1
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Bài 1:
a) Ta có: \(\left(15x^2\cdot y^2\cdot z\right):3xyz\)
\(=\dfrac{15x^2y^2z}{3xyz}\)
\(=5xy\)
b) Ta có: \(3x^2\cdot\left(5x^2-4x+3\right)\)
\(=3x^2\cdot5x^2-3x^2\cdot4x+3x^2\cdot3\)
\(=15x^4-12x^3+9x^2\)
c) Ta có: \(\left(2x^2-3x\right):\left(x-4\right)\)
\(=\dfrac{2x^2-8x+5x-20+20}{x-4}\)
\(=\dfrac{2x\left(x-4\right)+5\left(x-4\right)+20}{x-4}\)
\(=2x+5+\dfrac{20}{x-4}\)
d) Ta có: \(-5xy\cdot\left(3x^2y-5xy+y^2\right)\)
\(=-5xy\cdot3x^2y+5xy\cdot5xy-5xy\cdot y^2\)
\(=-15x^3y^2+25x^2y^2-5xy^3\)
![](https://rs.olm.vn/images/avt/0.png?1311)
`#3107`
`a.`
`4x^2 - 6x = 2x(2x - 3)`
`b.`
`9x^4y^3 + 3x^2y^4 = 3x^2y^2(3x^2y + y^2)`
`c.`
`x^3 - 2x^2 + 5x`
`= x(x^2 - 2x + 5)`
a) 4x² - 6x
= 2x(2x - 3)
b) 9x⁴y³ + 3x²y⁴
= 3x²y³(3x² + 3y)
c) x³ - 2x² + 5x
= x(x² - 2x + 5)
![](https://rs.olm.vn/images/avt/0.png?1311)
\(A=\left(5x^5+5x^4\right):5x^2-\left(2x^4-8x^2-6x+12\right):\left(2x-4\right)\)
Phép chia thứ nhất:
\(\left(5x^5+5x^4\right):5x^2=x^3+x^2\)
Phép chia thứ hai:
Vậy A = ( x^3 + x^2 ) - ( x^3 + 2x^2 - 3 ) = -x^2 + 3
Với x = -2 thì: A = -(-2)^2 + 3 = -4 + 3 = -1
B) bạn làm tương tự nhé
![](https://rs.olm.vn/images/avt/0.png?1311)
a.( 5x2-4x).(x-3)=5x3-15x2-4x2+12x=5x3-11x2+12x
b.(2-3xy).(3x4+4y2+5xy)=6x4+8y2+10xy-9x5y-12xy3-15x2y2
c.(-3x2+x+1).(x2+x-5)=-3x4-3x3+15+x3+x2-5x+x2+x-5=-3x4-2x3+2x-4x+10
b: =(x-2)(x+2)
\(a,3x^2y-6x=3x\left(xy-2\right)\)
\(b,x^2-4=x^2-2^2=\left(x-2\right)\left(x+2\right)\)
\(c,5x^2+5xy-x^2-2xy-y^2\)
\(=5x\left(x+y\right)-\left(x+y\right)\left(x+y\right)\)
\(=\left(x+y\right)\left(5x-x+y\right)\)
\(=\left(x+y\right)\left(4x+y\right)\)