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19 tháng 8 2020

a) \(-x-y^2+x^2-y\)

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

\(=\left(x-y\right)\left(x+y\right)-\left(x+y\right).1\)

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

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

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

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

c) \(x^2-5x+5y-y^2\)

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

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

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

d) \(5x^3-5x^2y-10x^2+10xy\)

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

\(=5x\left[x\left(x-y\right)-2\left(x-y\right)\right]\)

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

e) \(27x^3-8y^3\)

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

\(=\left(3x-2y\right)\left[\left(3x\right)^2+3x2y+\left(2y\right)^2\right]\)

\(=\left(3x-2y\right)\left(9x^2+6xy+4y^2\right)\)

f) \(x^2-y^2-x-y\)

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

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

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

g) \(x^2-y^2-2xy+y^2\)

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

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

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

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

h) \(x^2-y^2+4-4x\)

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

\(=\left(x^2-2.2x+2^2\right)-y^2\)

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

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

i) \(x^6-y^6\)

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

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

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

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

19 tháng 8 2020

a, -x - y2 + x2 - y = (x2 - y2) - (x + y)

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

= (x + y)(x - y - 1)

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

= (x - 5)(x + y)
c, x2 - 5x + 5y - y2 = (x - y)(x + y) - 5(x - y)

= (x - y)(x + y - 5)
d, 5x3 - 5x2y - 10x2 + 10xy = 5x2(x - y) - 10x(x - y)

= 5x(x - y)(x - 2)
e, 27x3 - 8y3 = (3x - 2y)(9x2 + 6xy + 4y2)
f, x2 - y2 - x - y = (x - y)(x + y) - (x + y)

= (x + y)(x - y - 1)
g, x2 - y2 - 2xy + y2 = (x2 - 2xy + y2) - y2

= (x - y)2 - y2

= (x - y - y)(x - y + y) = x(x - 2y)
h, x2 - y2 + 4 - 4x = (x2 - 4x + 4) - y2

= (x - 2)2 - y2

= (x - y - 2)(x + y - 2)
i, x3 + 3x2 + 3x + 1 - 27z3 = (x + 1)3 - 27z3

= (x+1-3z)(x2+2x+1+3xz+3z+9z2)
k, 4x2 + 4x - 9y2 + 1 = (2x + 1)2 - 9y2

= (2x - 3y + 1)(2x + 3y + 1)
m, x2 - 3x + xy - 3y = x(x - 3) + y(x - 3)

= (x - 3)(x + y)

12 tháng 10 2019

a) \(x^4+4x^2-5=x^4+4x^2+4-9=\left(x^2+2\right)^2-3^2\)

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

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

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

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

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

e) \(5x^3-5x^2y-10x^2+10xy=5x^2\left(x-y\right)-10x\left(x-y\right)\)

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

f) \(27x^3-8y^3=\left(3x\right)^3-\left(2y\right)^3=\left(3x-2y\right)\left(9x^2+6xy+4y^2\right)\)

a: \(5x-20y=5\left(x-4y\right)\)

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

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

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

28 tháng 10 2021

\(1,=\left(x-3\right)\left(x+3\right)\\ 2,=\left(x-y\right)\left(5+a\right)\\ 3,=\left(x+3\right)^2\\ 4,=\left(x-y\right)\left(10x+7y\right)\\ 5,=5\left(x-3y\right)\\ 6,=\left(x-y\right)^2-z^2=\left(x-y-z\right)\left(x-y+z\right)\)

28 tháng 10 2021

bạn gõ lại công thức cho rõ đi, khó đọc quá

13 tháng 10 2019

a) \(\left(5x-4\right)^2-49x^2\)

\(=\left(5x-4\right)^2-\left(7x\right)^2\)

\(=\left(12x-4\right)\left(-2x-4\right)\)

\(=-6\left(3x-1\right)\left(x+2\right)\)

c) \(x^2-y^2-x+y\)

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

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

d)\(4x^2-9y^2+4x-6y\)

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

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

13 tháng 10 2019

e) \(-x^2+5x+2xy-5y-y^2\)

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

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

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

f) \(y^2\left(x^2+y\right)-zx^2-zy\)

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

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

16 tháng 12 2018

\(10x\left(x-y\right)-6y\left(y-x\right)\)

\(=10x\left(x-y\right)+6x\left(x-y\right)\)

\(=\left(10x+6x\right)\left(x-y\right)\)

\(c,3x^2+5y-3xy-5x\)

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

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

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

\(e,27+27x+9x^2=3\left(9+9x+x^2\right)\)

16 tháng 12 2018

\(f,8x^3-12x^2y+6xy^2-y^3\)

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

\(g,x^3+8y^3=x^3+\left(2y\right)^3\)

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

\(i,x^2-25-2xy+y^2\)

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

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

27 tháng 7 2023

a Đề sai: )

b

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

c

\(4x^2-y^2+4x+1\\ =\left(2x\right)^2+2.2x.1+1-y^2\\ =\left(2x+1\right)^2-y^2\\ =\left(2x+1-y\right)\left(2x+1+y\right)\)

d

\(x^4+2x^3+x^2\\ =x^4+x^3+x^3+x^2\\ =x^3\left(x+1\right)+x^2\left(x+1\right)\\ =\left(x^3+x^2\right)\left(x+1\right)\)

e

\(5x^2-10xy+5y^2-5z^2\\ =5\left(x^2-2xy+y^2-z^2\right)\\ =5\left[\left(x-y\right)^2-z^2\right]\\ =5\left(x-y-z\right)\left(x-y+z\right)\)

c: =(2x+1)^2-y^2

=(2x+1+y)(2x+1-y)

d: =x^2(x^2+2x+1)

=x^2(x+1)^2

e: =5(x^2-2xy+y^2-z^2)

=5[(x-y)^2-z^2]

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