Bài 2: 

a: \(3x^2-3xy=3x\left(x-y\right)\)

b: \(x^2-4y^2=\left(x-2y\right)\left(x+2y\right)\)

c: \(3x-3y+xy-y^2=\left(x-y\right)\left(3+y\right)\)

d: \(x^2-y^2+2y-1=\left(x-y+1\right)\left(x+y-1\right)\)

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a: \(N=\dfrac{3x^5-4x^4+6x^3}{-2x^2}=-\dfrac{3}{2}x^3+2x^2-3x\)

b: \(N=\dfrac{\left(6x^4y^5-3x^3y^4+\dfrac{1}{2}x^4y^3z\right)}{-\dfrac{1}{3}x^2y^3}=-18x^2y^2+9xy-\dfrac{3}{2}x^2z\)

c: \(\Leftrightarrow N\cdot\left(y-x\right)=\left(x-y\right)^3\)

\(\Leftrightarrow N=\dfrac{\left(x-y\right)^3}{y-x}=-\left(y-x\right)^2\)

d: \(\Leftrightarrow N\cdot\left(y^2-x^2\right)=\left(y^2-x^2\right)^2\)

hay \(N=y^2-x^2\)

\(\text{a) }\left(x-1\right)\left(x^2+y\right)-\left(x^2-y\right)\left(x-2\right)-x\left(x+2y\right)+3\left(y-5\right)\)

\(=\left(x^3+xy-x^2-y\right)-\left(x^3-2x^2-xy+2y\right)-\left(x^2+2xy\right)+\left(3y-15\right)\)

\(=x^3+xy-x^2-y-x^3+2x^2+xy-2y-x^2-2xy+3y-15\)

\(=\left(x^3+x^3\right)+\left(-x^2+2x^2-x^2\right)+\left(xy+xy-2xy\right)+\left(-y-2y+3y\right)-15\)

\(=0+0+0+0-15\)

\(=-15\)

\(\text{b) }6\left(x^3y+x-3\right)-6x\left(2xy^3+1\right)-3x^2y\left(2x-4y^2\right)\)

\(=\left(6x^3y+6x-18\right)-\left(12x^2y^3+6x\right)-\left(6x^3y-12x^2y^3\right)\)

\(=6x^3y+6x-18-12x^2y^3-6x-6x^3y+12x^2y^3\)

\(=\left(6x^3y-6x^3y\right)+\left(6x-6x\right)+\left(-12x^2y^3+12x^2y^3\right)-18\)

\(=0+0+0-18\)

\(=-18\)

\(\text{c) }\left(x^2+2xy+4y^2\right)\left(x-2y\right)-6\left(\frac{1}{2}-\frac{4}{3}y^3\right)\)

\(=\left(x^3-2x^2y+2x^2y-4xy^2+4xy^2-8y^3\right)-\left(3-8y^3\right)\)

\(=\left(x^3-8y^3\right)-\left(3-8y^3\right)\)

\(=x^3-8y^3-3+8y^3\)

\(=x^3-3\)

giúp mình vs mn ơi

Bài 1: 

a, (\(x\) - 4).(\(x\) + 4) - (5 - \(x\)).(\(x\) + 1)

= \(x^2\) -  16 - 5\(x\) - 5 + \(x^2\) + \(x\) 

= (\(x^2\) + \(x^2\)) - (5\(x\) - \(x\)) - (16 + 5)

= 2\(x^2\) - 4\(x\) - 21

b, (3\(x^2\) - 2\(xy\) + 4) + (5\(xy\) - 6\(x^2\) - 7)

=  3\(x^2\) - 2\(xy\) + 4 + 5\(xy\) - 6\(x^2\) - 7

= (3\(x^2\) - 6\(x^2\)) + (5\(xy\) - 2\(xy\)) - (7 - 4)

= - 3\(x^2\) + 3\(xy\) - 3

Bài 2:

a, 3\(x^2\).(2\(x\) + y) - 2y(4\(x^2\) - y)

= 6\(x^3\) + 3\(x^2\).y - 8y\(x^2\) + 2y²

= 6\(x^3\) - (8\(x^2\)y - 3\(x^2\)y) + 2y²

= 6\(x^3\) - 5\(x^2\)y + 2y²

\(12x^2y-18xy^2-30y^2=6y\left(2x^2-3xy-5y\right)\)

\(d,5\left(x-y\right)-y\left(x-y\right)=\left(5-y\right)\left(x-y\right)\)

Bài 1:
a) (2x - y) + (2x - y) + (2x - y) + 3y
= 3(2x - y) + 3y
= 3(2x - y + 3y)
= 3(2x + 2y)
= 3.2(x + y)
= 6(x + y)

b) (x + 2y) + (x - 2y) + (8x - 3y)
= x + 2y + x - 2y + 8x - 3y
= 9x - 3y
= 3(3x - y)

c) (x + 2y) - 2(x - 2y) - (2x - 3y)
= x + 2y - 2x + 4y - 2x + 3y
= 9y - 3x
= 3(3y - x)

Bài 2:
M + 2(x² - 4y²) + Q = 6x² - 4xy + 5y² + P
M + 2x² - 8y²   -3x² + 7xy - 2y² = 6x² - 4xy + 5y² + 9x² - 6xy + 3y²
M + 2x² - 3x² - 6x² - 9x² - 8y² - 2y² - 5y² - 3y² + 7xy + 4xy + 6xy = 0
M - 16x² - 18y² + 17xy = 0
M = 16x² + 18y² - 17xy