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21 tháng 7 2018

\(a,\left(3x-1\right)^2-16=\left(3x-5\right)\left(3x+3\right)=3\left(x+1\right)\left(3x-5\right)\)

\(b,\left(5x-4\right)^2-49x^2=\left(12x-4\right)\left(-2x-4\right)=4\left(3x-1\right)\left(-2\right)\left(x+2\right)=-8\left(3x-1\right)\left(x+2\right)\)\(c,\left(2x+5\right)^2-\left(x-9\right)^2=\left(3x-4\right)\left(x+14\right)\)

21 tháng 7 2018

a,\(\left(3x+1\right)^2-16=\left(3x-1-16\right)\left(3x-1+16\right)\\ =\left(3x-17\right)\left(3x+15\right)\)

21 tháng 8 2017

a)\(\left(3x-1\right)^2-16=\left(3x-1-16\right)\left(3x-1+16\right)\)

                                     \(=\left(3x-17\right)\left(3x+15\right)\)

c)\(\left(2x+5\right)^2-\left(x-9\right)^2=\left(2x+5+x-9\right)\left(2x+5-x+9\right)\)

                                                 \(=\left(x-4\right)\left(x+14\right)\)

      Aps dungj t/c a2 - b2 = ( a-b)(a+b)

a) Ta có: \(\left(3x-1\right)^2-16\)

\(=\left(3x-1-4\right)\left(3x-1+4\right)\)

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

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

b) Ta có: \(\left(5x-4\right)^2-49x^2\)

\(=\left(5x-4-7x\right)\left(5x-4+7x\right)\)

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

\(=-2\left(x+2\right)\cdot4\cdot\left(3x-1\right)\)

\(=-8\left(x+2\right)\left(3x-1\right)\)

c) Ta có: \(\left(2x+5\right)^2-\left(x-9\right)^2\)

\(=\left(2x+5-x+9\right)\left(2x+5+x-9\right)\)

\(=\left(x+14\right)\left(3x-4\right)\)

d) Ta có: \(\left(3x+1\right)^2-4\left(x-2\right)^2\)

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

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

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

e) Ta có: \(9\left(2x+3\right)^2-4\left(x+1\right)^2\)

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

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

\(=\left(4x+7\right)\left(8x+11\right)\)

f) Ta có: \(4b^2c^2-\left(b^2+c^2-a^2\right)^2\)

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

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

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

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

g) Ta có: \(\left(ax+by\right)^2-\left(ay+bx\right)^2\)

\(=\left(ax+by-ay-bx\right)\left(ax+by+ay+bx\right)\)

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

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

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

h) Ta có: \(\left(a^2+b^2-5\right)^2-4\left(ab+2\right)^2\)

\(=\left(a^2+b^2-5\right)^2-\left(2ab+4\right)^2\)

\(=\left(a^2+b^2-5+2ab+4\right)\left(a^2+b^2-5-2ab-4\right)\)

\(=\left[\left(a^2+2ab+b^2\right)-1\right]\left[\left(a^2-2ab+b^2\right)-9\right]\)

\(=\left(a+b-1\right)\left(a+b+1\right)\left(a-b-3\right)\left(a-b+3\right)\)

i) Ta có: \(\left(4x^2-3x-18\right)^2-\left(4x^2+3x\right)^2\)

\(=\left(4x^2-3x-18-4x^2-3x\right)\left(4x^2-3x-18+4x^2+3x\right)\)

\(=\left(-6x-18\right)\left(8x^2-18\right)\)

\(=-6\left(x+3\right)\cdot2\left(x^2-9\right)\)

\(=-12\left(x+3\right)^2\cdot\left(x-3\right)\)

k) Ta có: \(9\left(x+y-1\right)^2-4\left(2x+3y+1\right)^2\)

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

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

\(=\left(-x-3y-5\right)\left(7x+9y-1\right)\)

l) Ta có: \(-4x^2+12xy-9y^2+25\)

\(=-\left(4x^2-12xy+9y^2-25\right)\)

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

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

m) Ta có: \(x^2-2xy+y^2-4m^2+4mn-n^2\)

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

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

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

a) Ta có: \(\left(4x^2-3x-18\right)^2-\left(4x^2+3x\right)^2\)

\(=\left(4x^2-3x-18-4x^2-3x\right)\left(4x^2-3x-18+4x^2+3x\right)\)

\(=\left(-6x-18\right)\left(8x^2-18\right)\)

\(=-6\left(x+3\right)\cdot2\left(4x^2-9\right)\)

\(=-12\left(x+3\right)\left(2x-3\right)\left(2x+3\right)\)

b) Ta có: \(9\left(x+y-1\right)^2-4\left(2x+3y+1\right)^2\)

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

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

\(=-\left(x+3y+5\right)\left(7x+9y-1\right)\)

c) Ta có: \(-4x^2+12xy-9y^2+25\)

\(=-\left(4x^2-12xy+9y^2-25\right)\)

\(=-\left[\left(2x-3y\right)^2-25\right]\)

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

d) Ta có: \(x^2-2xy+y^2-4m^2+4mn-n^2\)

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

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

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

7 tháng 10 2020

Mike ko đủ thời gian nha😅x.lỗi

7 tháng 10 2020

a) ( 3x - 1 )2 - 16 = ( 3x - 1 )2 - 42 = ( 3x - 1 - 4 )( 3x - 1 + 4 ) = ( 3x - 5 )( 3x + 3 ) = 3( 3x - 5 )( x + 1 )

b) ( 5x - 4 )2 - 49x2 = ( 5x - 4 )2 - ( 7x )2 = ( 5x - 4 - 7x )( 5x - 4 + 7x ) = ( -2x - 4 )( 12x - 4 ) = -2( x + 2 ).4( 3x - 1 ) = -8( x + 2 )( 3x - 1 )

c) ( 2x + 5 )2 - ( x - 9 )2 = [ ( 2x + 5 ) - ( x - 9 ) ][ ( 2x + 5 ) + ( x - 9 ) ] = ( 2x + 5 - x + 9 )( 2x + 5 + x - 9 ) = ( x + 14 )( 3x - 4 )

d) ( 3x + 1 )2 - 4( x - 2 )2 = ( 3x + 1 )2 - 22( x - 2 )2 = ( 3x + 1 )2 - [ 2( x - 2 ) ]2 = ( 3x + 1 )2 - ( 2x - 4 )2 = [ ( 3x + 1 ) - ( 2x - 4 ) ][ ( 3x + 1 ) + ( 2x - 4 ) ] = ( 3x + 1 - 2x + 4 )( 3x + 1 + 2x - 4 ) = ( x + 5 )( 5x - 3 )

e) 9( 2x + 3 )2 - 4( x + 1 )2 = 32( 2x + 3 )2 - 22( x + 1 )2 = [ 3( 2x + 3 ) ]2 - [ 2( x + 1 ) ]2 = ( 6x + 9 )2 - ( 2x + 2 )2 = [ ( 6x + 9 ) - ( 2x + 2 ) ][ ( 6x + 9 ) + ( 2x + 2 ) ] = ( 6x + 9 - 2x - 2 )( 6x + 9 + 2x + 2 ) = ( 4x + 7 )( 8x + 11 )

f) 4b2c2 - ( b2 + c2 - a2 )2 = ( 2bc )2 - ( b2 + c2 - a2 )2 = [ 2bc - ( b2 + c2 - a2 ) ][ 2bc + ( b2 + c2 - a2 ] = ( 2bc - b2 - c2 + a2 )( 2bc + b2+ c2 - a2 ) = [ a2 - ( b2 - 2bc + c2 ) ][ ( b2 + 2bc + c2 ) - a2 ] = [ a2 - ( b - c )2 ][ ( b + c )2 - a2 ] = ( a - b + c )( a + b - c )( b + c - a )( b + c + a )

7 tháng 10 2020

g) ( ax + by )2 - ( ay + bx )2 

= [ ( ax + by ) - ( ay + bx ) ][ ( ax + by ) + ( ay + bx ) ]

= ( ax + by - ay - bx )( ax + by + ay + bx )

= [ a( x - y ) - b( x - y ) ][ a( x + y ) + b( x + y ) ]

= ( a - b )( x - y )( x + y )( a + b )

h) ( a2 + b2 - 5 )2 - 4( ab + 2 )2 

= ( a2 + b2 - 5 )2 - 22( ab + 2 )2 

= ( a2 + b2 - 5 )2 - [ 2( ab + 2 ) ]2 

= ( a2 + b2 - 5 )2 - ( 2ab + 4 )2 

= [ ( a2 + b2 - 5 ) - ( 2ab + 4 ) ][ ( a2 + b2 - 5 ) + ( 2ab + 4 ) ]

= ( a2 + b2 - 5 - 2ab - 4 )( a2 + b2 - 5 + 2ab + 4 )

= [ ( a2 - 2ab + b2 ) - 9 ][ ( a2 + 2ab + b2 ) - 1 ]

= [ ( a - b )2 - 32 ][ ( a + b )2 - 12 ]

= ( a - b - 3 )( a - b + 3 )( a + b - 1 )( a + b + 1 )

i) ( 4x2 - 3x - 18 )2 - ( 4x2 + 3x )2

= [ ( 4x2 - 3x - 18 ) - ( 4x2 + 3x ) ][ ( 4x2 - 3x - 18 ) + ( 4x2 + 3x ) ]

= ( 4x2 - 3x - 18 - 4x2 - 3x )( 4x2 - 3x - 18 + 4x2 + 3x )

= ( -6x - 18 )( 8x2 - 18 )

= -6( x + 3 ).2( 4x2 - 9 )

= -12( x + 3 )( 2x - 3 )( 2x + 3 )

k) 9( x + y - 1 )2 - 4( 2x + 3y + 1 )2

= 32( x + y - 1 )2 - 22( 2x + 3y + 1 )2

= [ 3( x + y - 1 ) ]2 - [ 2( 2x + 3y + 1 ) ]2

= ( 3x + 3y - 3 )2 - ( 4x + 6y + 2 )2

= [ ( 3x + 3y - 3 ) - ( 4x + 6y + 2 ) ][ ( 3x + 3y - 3 ) + ( 4x + 6y + 2 ) ]

= ( 3x + 3y - 3 - 4x - 6y - 2 )( 3x + 3y - 3 + 4x + 6y + 2 )

= ( -x - 3y - 5 )( 7x + 9y - 1 )

l) -4x2 + 12xy - 9y2 + 25

= 25 - ( 4x2 - 12xy + 9y2 )

= 52 - ( 2x - 3y )2

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

m) x2 - 2xy + y2 - 4m2 + 4mn - n2

= ( x2 - 2xy + y2 ) - ( 4m2 - 4mn + n2 )

= ( x - y )2 - ( 2m - n )2

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

16 tháng 8 2018

Mk chỉ lm 2 phần đầu thôi ,bn tham khảo nha!!!

\(a,\left(3x-1\right)^2-16=\left(3x-1+4\right)\left(3x-1-4\right)=\left(3x+3\right)\left(3x-5\right)=3\left(x+1\right)\left(3x-5\right)\)

\(b,\left(5x-4\right)^2-49x^2=\left(5x-4+7x\right)\left(5x-4-7x\right)\)

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

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

\(=-8\left(3x-1\right)\left(x+2\right)\)

=.= hok tốt!!

30 tháng 9 2018

\(\left(3x-1\right)^2-16\)

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

\(=\left(3x-1-4\right)\left(3x-1+4\right)\)

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

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

4 tháng 11 2018

a) \(2x^2-2y^2\)

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

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

b) \(x^2-4x+4\)

\(=x^2-2\cdot x\cdot2+2^2\)

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

c) \(x^2+2x+1-y^2\)

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

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

d) \(x^2-4x\)

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

e) \(x^2+10x+25\)

\(=x^2+2\cdot x\cdot5+5^2\)

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

g) \(x^2-2xy+y^2-9\)

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

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

h) \(2x^2-2\)

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

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

i) \(5x^2-5xy+9x-9y\)

\(=5x\left(x-y\right)+9\left(x-y\right)\)

\(=\left(x-y\right)\left(5x+9\right)\)

k) \(y^2-4y+4-x^2\)

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

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

l) \(x^2-16\)

\(=x^2-4^2\)

\(=\left(x-4\right)\left(x+4\right)\)

m) \(3x^2-3xy+2x-2y\)

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

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

o) \(3x^4-6x^3+3x^2\)

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

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

4 tháng 11 2018

a) 2x2 - 2y2

 = (2x - 2y)(2x + 2y)

 = 4(x - y)(x + y)

b) x2 - 4x + 4

 = (x - 2)2

c) x+ 2x + 1 - y2

 = (x + 1)2 - y2

 = (x + 1 - y)(x + 1 + y)

d) x2 - 4x 

 = x(x - 4)

e) x+10x + 25

 = (x + 5)2

g) x2 - 2xy + y2 - 9

= (x - y)2 - 32

 = (x - y - 3)(x - y + 3)

h) 2x2 - 2

= 2(x2 - 1) 

 = 2(x - 1)(x + 1)

i) 5x- 5xy + 9x - 9y

  = 5x(x - y) + 9(x- y)

 = (5x + 9)(x - y)

k) y2 - 4y + 4 - x2

 = (y - 2)2 - x2

 = (y - 2 - x)(y - 2 + x)

l) x- 16

 = x- 42

 = (x - 4)(x + 4)

m) 3x2 - 3xy + 2x -2y

 = 3x(x - y) +2(x-y)

 = (3x + 2)(x - y)

o) 3x- 6x+ 3x2

 = 3x4 - 3x3 - 3x3 + 3x2

 = 3x3(x - 1) - 3x2(x - 1)

 = (3x- 3x2)(x - 1)

 = 3x2(x - 1)(x - 1)

 = 3x2.(x - 1)2

30 tháng 7 2020

cái cuối hằng đẳng thức là xong mà bạn

30 tháng 7 2020

a) \(\left(4x^2-3x-18\right)^2-\left(4x^2+3x\right)^2\)

\(=\left(4x^2-3x-18-4x^2-3x\right)\left(4x^2-3x-18+4x^2+3x\right)\)

\(=\left(-6x-18\right)\left(8x^2-18\right)\)

b) \(9\left(x+y-1\right)^2-4\left(2x+3y+1\right)^2\)

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

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

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

\(=\left(7x+9y-1\right)\left(-x-3y-5\right)\)

c) \(-4x^2+12xy-9y^2+25\)

\(=-\left(2x\right)^2+2.2x.3y-\left(3y\right)^2+5^2\)

\(=-\left[\left(2x\right)^2-2.2x.3y+\left(3y\right)^2-5^2\right]\)

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

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

d) \(x^2-2xy+y^2-4m^2+4mn-n^2\)

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

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

\(=\left(x-y-n\right)\left(x-y+n\right)-4m\left(m-n\right)\)

6 tháng 10 2021

\(a,=\left(3x-5\right)\left(3x+3\right)=3\left(x+1\right)\left(3x-5\right)\\ b,=\left(5x-4-7x\right)\left(5x-4+7x\right)=\left(-2x-4\right)\left(12x-4\right)\\ =-8\left(x+2\right)\left(x-3\right)\\ c,=\left(2x+5-x+9\right)\left(2x+5+x-9\right)\\ =\left(x+14\right)\left(3x-4\right)\\ d,=\left(3x+1-2x+4\right)\left(3x+1+2x-4\right)\\ =\left(x+5\right)\left(5x-3\right)\\ e,=\left(6x+9-2x-2\right)\left(6x+9+2x+2\right)\\ =\left(4x+7\right)\left(8x+11\right)\\ f,=\left(2bc-b^2-c^2+a^2\right)\left(2bc+b^2+c^2-a^2\right)\\ =\left[a^2-\left(b-c\right)^2\right]\left[\left(b+c\right)^2-a^2\right]\\ =\left(a-b+c\right)\left(a+b-c\right)\left(b+c-a\right)\left(b+c+a\right)\\ g,=\left(ax+by-ay-bx\right)\left(ax+by+ay+bx\right)\\ =\left(a-b\right)\left(x-y\right)\left(a+b\right)\left(x+y\right)\)

\(h,=\left(a^2+b^2-5-2ab-4\right)\left(a^2+b^2-5+2ab+4\right)\\ =\left[\left(a-b\right)^2-9\right]\left[\left(a+b\right)^2-1\right]\\ =\left(a-b-3\right)\left(a-b+3\right)\left(a+b-1\right)\left(a+b+1\right)\)

a: \(\left(3x-1\right)^2-16\)

\(=\left(3x-1-4\right)\left(3x-1+4\right)\)

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

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

b: \(\left(5x-4\right)^2-49x^2\)

\(=\left(5x-4-7x\right)\left(5x-4+7x\right)\)

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

\(=-8\left(x+2\right)\left(3x-1\right)\)