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a) \(5x-20y\\ =5\left(x-4y\right)\)

b) \(5x\left(x-1\right)-3x\left(x-1\right)\\ =\left(5x-3x\right)\left(x-1\right)\\ =2x\left(x-1\right)\)

c) \(x\left(x+y\right)-5x-5y\\ =x\left(x+y\right)-\left(5x+5y\right)\\ =x\left(x+y\right)-5\left(x+y\right)\\ =\left(x+y\right)\left(x-5\right)\)

29 tháng 5 2017

a) 5x-20y=5(x-4y)

b) 5x(x-1)-3x(x-1)

= (x-1)(5x-3x)

c) x(x+y)-5x-5y

=x(x+y)-5(x+y)

=(x+y)(x-5)

16 tháng 7 2017

a.

\(5x^2\left(x-2y\right)-15x\left(x-2y\right)\)

\(=\left(x-2y\right)\left(5x^2-15x\right)\)

\(=5x\left(x-2y\right)\left(x-3\right)\)

b. 

\(3\left(x-y\right)-5x\left(y-x\right)\)

\(=3\left(x-y\right)+5x\left(x-y\right)\)

\(=\left(x-y\right)\left(3+5x\right)\)

16 tháng 7 2017

\(a,5x^2\left(x-2y\right)-15x\left(x-2y\right)\) 

\(=5x\left(x-2y\right)\left(x-3\right)\) 

\(b,3\left(x-y\right)-5x\left(y-x\right)=3\left(x-y\right)+5x\left(x-y\right)\) 

\(=\left(x-y\right)\left(3+5x\right)\)

Chúc bạn học tốt!

1 tháng 11 2016

Đây, bản full đây thím, tớ thực sự đã kiên nhẫn lắm đấy ...

a)\(4\left(x^2-y^2\right)-8\left(x-ay\right)-4\left(a^2-1\right)=4\left(x^2-y^2-2x+2ay-a^2+1\right)\)

\(=4\left[\left(x^2-2x+1\right)-\left(a^2-2ay+y^2\right)\right]\)

\(=4\left[\left(x-1\right)^2-\left(a-y\right)^2\right]\)

\(=4\left(x-1-a+y\right)\left(x-1+a-y\right)\)

b)\(\left(x+y\right)^3-1-3xy\left(x+y-1\right)\)

\(=\left(x+y-1\right)\left[\left(x+y\right)^2+x+y+1\right]-3xy\left(x+y-1\right)\)

\(=\left(x+y-1\right)\left(x^2+2xy+y^2+x+y+1\right)-3xy\left(x+y-1\right)\)

\(=\left(x+y-1\right)\left(x^2+2xy+y^2+x+y+1-3xy\right)\)

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

c)\(x^3-1+5x^2-5+3x-3=\left(x-1\right)\left(x^2+x+1\right)+5\left(x^2-1\right)+3\left(x-1\right)\)

\(=\left(x-1\right)\left(x^2+x+1\right)+5\left(x-1\right)\left(x+1\right)+3\left(x-1\right)\)

\(=\left(x-1\right)\left(x^2+x+1\right)+\left(x-1\right)\left(5x+5\right)+3\left(x-1\right)\)

\(=\left(x-1\right)\left(x^2+x+1+5x+5+3\right)\)

\(=\left(x-1\right)\left(x^2+6x+9\right)\)

\(=\left(x-1\right)\left(x+3\right)^2\)

d)\(a^5+a^4+a^3+a^2+a+1=a^4\left(a+1\right)+a^2\left(a+1\right)+\left(a+1\right)\)

\(=\left(a+1\right)\left(a^4+a^2+1\right)\)

\(=\left(a+1\right)\left(a^4+2a^2+1-a^2\right)\)

\(=\left(a+1\right)\left[\left(a^2+1\right)^2-a^2\right]\)

\(=\left(a+1\right)\left(a^2-a+1\right)\left(a^2+a+1\right)\)

e)\(x^3-3x^2+3x-1-y^3=\left(x-1\right)^3-y^3\)

\(=\left(x-1-y\right)\left[\left(x-1\right)^2+\left(x-1\right)y+y^2\right]\)

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

f)\(5x^3-3x^2y-45xy^2+27y^3=5x\left(x^2-9y^2\right)-3y\left(x^2-9y^2\right)\)

\(=\left(x^2-9y^2\right)\left(5x-3y\right)\)

\(=\left(x-3y\right)\left(x+3y\right)\left(5x-3y\right)\)

g)\(3x^2\left(a-b+c\right)+36xy\left(a-b+c\right)+108y^2\left(a-b+c\right)\)

\(=\left(a-b+c\right)\left(3x^2+36xy+108y^2\right)\)

\(=3\left(a-b+c\right)\left(x^2+12xy+36y^2\right)\)

\(=3\left(a-b+c\right)\left(x+6y\right)^2\)

1 tháng 11 2016

a/ \(4\left(x^2-y^2\right)-8\left(x-ay\right)-4\left(a^2-1\right)\)

\(=\left(4x^2-8x+4\right)-\left(4y^2-8ay+4a^2\right)\)

\(=\left(2x-2\right)^2-\left(2y-2a\right)^2=\left(2x-2+2y-2a\right)\left(2x-2-2y+2a\right)\)

b/ \(\left(x+y\right)^3-1-3xy\left(x+y-1\right)=\left(x+y-1\right)\left(x^2+y^2+2xy+x+y+1\right)-3xy\left(x+y-1\right)\)

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

Giải giúp bạn 2 bài tiêu biểu thôi nha

1a) (x - 2y) (x2 - 2xy + y2)

= (x - 2y) (x - y)2

= x2 - xy - 2xy + 2y2

= (x2 - xy) - (2xy - 2y2)

= x (x - y) - 2y (x - y)

= (x - y) (x - 2y)

2a) x (x - 3) - y (3 - x)

= x (x - 3) + y (x - 3)

= (x - 3) (x + y)

b) 3x2 - 5x - 3xy + 5y

= (3x2 - 3xy) - (5x - 5y)

= 3x (x - y) - 5 (x - y)

= (x - y) (3x - 5)

3) 12x (3 - 4x) + 7 (4x - 3) = 0

12x (3 - 4x) - 7 (3 - 4x) = 0

(3 - 4x) (12x - 7) = 0

=> 3 - 4x = 0 hoặc 12x - 7 = 0

* 3 - 4x = 0 => x = \(\frac{3}{4}\)

* 12x - 7 = 0 => x = \(\frac{7}{12}\)

Vậy x =\(\frac{3}{4}\)hoặc x =\(\frac{7}{12}\)

5 tháng 8 2018

1) \(\left(5x-4\right)\left(4x-5\right)+\left(5x-1\right)\left(x+4\right)+3\left(3x-2\right)\)

\(=20x^2-41x+20+\left(5x-1\right)\left(x+4\right)+3\left(3x-2\right)\)

\(=20x^2-41+20+5x^2+19x-4+3\left(3x-2\right)\)

\(=20x^2-41x+20+5x^2+19x-4+9x-4\)

\(=25x^2-13x+10\)

2) \(\left(5x-4\right)^2+\left(16-25x^2\right)+\left(5x+4\right)\left(3x+2\right)\)

\(=\left(5x-4\right)^2+16-25x^2+\left(5x-4\right)\left(3x+2\right)\)

\(=25x^2-40x+16^2-25x^2+\left(5x-4\right)\left(3x+2\right)\)

\(=25x^2-40x+16^2-25x^2+15x^2-2x-8\)

\(=15x^2-42x+24\)

15 tháng 6 2017

a) \(5x-5y+ax-ay\)

\(\Leftrightarrow\) \(\left(5x+ax\right)-\left(5y+ay\right)\)

\(\Leftrightarrow\) \(x\left(5+a\right)-y\left(5+a\right)\)

\(\Leftrightarrow\) \(\left(5+a\right)\left(x-y\right)\)

15 tháng 6 2017

b) \(a^3-a^2x-ay+xy\)

\(\Leftrightarrow\) \(a^2\left(a-x\right)-y\left(a-x\right)\)

\(\Leftrightarrow\) \(\left(a-x\right)\left(a^2-y\right)\)

\(x\left(x+y\right)-5x-5y\)

\(=x\left(x+y\right)-5\left(x+y\right)\)

\(=\left(x+y\right)\left(x-5\right)\)

2 tháng 8 2016

x(x+y)-5x-5y

= x.x+x.y-5x-5y

= x^2+x.y-5x-5y

= x.(x-5)-y.(x-5)

= (x-y).(x-5)

Đúng thì k nhak ^3^"""

25 tháng 6 2019

\(a.5x-20y\)

\(\Leftrightarrow5\left(x-4y\right)\)

\(b.14x^2y-21xy^2+28x^2y^2\)

\(\Leftrightarrow7xy\left(2x-3y+4xy\right)\)

\(c.x\left(x+y\right)-5x-5y\)

\(\Leftrightarrow x\left(x+y\right)-5\left(x+y\right)\)

\(\Leftrightarrow\left(x-5\right)\left(x+y\right)\)

\(d.10x\left(x-y\right)-8y\left(y-x\right)\)

\(\Leftrightarrow10x\left(x-y\right)+8y\left(x-y\right)\)

\(\Leftrightarrow2\left(5x+4y\right)\left(x-y\right)\)

31 tháng 8 2018

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

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

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

b)\(\left(x^2-3x-1\right)^2-12\left(x^2-3x-1\right)+27\)

Đặt x^2 - 3x - 1 = A

\(\Rightarrow A^2-12A+27=\left(A^2-12A+36\right)-9\)

\(=\left(A-6\right)^2-9=\left(A-6-3\right)\left(A-6+3\right)\)

\(=\left(A-9\right)\left(A-3\right)\)

Hay \(=\left(x^2-3x-1-9\right)\left(x^2-3x-1-3\right)\)

\(=\left(x^2-3x-10\right)\left(x^2-3x-4\right)\)

\(=\left(x-5\right)\left(x+2\right)\left(x-4\right)\left(x+1\right)\)

c)\(x^3-x^2-5x+125\)

\(=\left(x^3+5^3\right)-\left(x^2+5x\right)\)

\(=\left(x+5\right)\left(x^2-5x+25\right)-x\left(x+5\right)\)

\(=\left(x+5\right)\left(x^2-5x+25-x\right)\)

\(=\left(x+5\right)\left(x^2-6x+25\right)\)

d)\(xy\left(x+y\right)+yz\left(y+z\right)+zx\left(z+x\right)+2xyz\)

\(=\left(x+y\right)\left(y+z\right)\left(x+z\right)\)

Mình có việc bận nên chỉ đưa được kết quả ý d)  thật lòng mong các bạn tự tham khảo và giải

13 tháng 8 2019

\(\left(a-b\right)^2-\left(b-a\right)\)

\(=\left(a-b\right)^2+\left(a-b\right)\)

\(=\left(a-b\right)\left(a-b+1\right)\)

13 tháng 8 2019

\(5\left(a+b\right)^2-\left(a+b\right)\left(a-b\right)\)

\(=\left(a+b\right)\left[5\left(a+b\right)-\left(a-b\right)\right]\)

\(=\left(a+b\right)\left[5a+5b-a+b\right]\)

\(=\left(a+b\right)\left[4a+6b\right]\)