\(4\left(x^2-y^2\right)-8\left(x-ay\right)-4\lef...">
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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

29 tháng 6 2018

BÀI 1:

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

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

\(=\left(3a+3b\right)\left(a-b\right)=3\left(a+b\right)\left(a-b\right)\)

c) \(\left(a^3-b^3\right)+\left(a-b\right)^2=\left(a-b\right)\left(a^2+ab+b^2\right)+\left(a-b\right)^2\)

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

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

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

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

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

h) ktra lại đề

m) \(\left(x-a\right)^4-\left(x+a\right)^4=-8ax\left(a^2+x^2\right)\)

29 tháng 6 2018

a ) x^4 + 2x^2y + y^2 

   Dùng hằng đẳng thức ( a + b )^2 = a^2 +2ab + b^2

   = ( x^2 + y )^2

b ) ( 2a + b )^2 - ( 2b + a )^2

   = ( 4a^2 + 4ab + b^2 ) - ( 4b^2 + 4ab + a^2 )

   = 4a^2 + 4ab + b^2 - 4b^2 - 4ab - a^2

   = 3a^2- 3b^2

   = 3( a^2 - b^2 ) 

23 tháng 8 2016

1 ) \(a\left(m+n\right)+b\left(m+n\right)\)

   \(=\left(a+b\right)\left(m+n\right)\)

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

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

   \(=\left[\left(a-b\right).\left(a+3\right)\right]\left(x+y\right)\)

3 ) \(6a^2-3a+12ab\)

   \(=3a.2a-3a+3a.4b\)

   \(=3a.\left(2a-1+4b\right)\)

4 ) \(2x^2y^4-2x^4y^2+6x^3y^3\)

   \(=2x^2y^2.y^2-2x^2y^2.x^2+2x^2y^2.3xy\)

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

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

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

      \(=\left(x+y\right)^2.y\)

      

 

23 tháng 8 2016

1)a(m+n)+b(m+n)

=(a+b)(m+n)

2)a2(x+y)-b2(x+y)

=(a2-b2)(x+y)

3)6a2-3a+12ab

=3a.2a-3a.(1-4b)

=3a.(2a-1+4b)

5)(x+y)3-x(x+y)2

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

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