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a) x^2 - 2xy + y^2 - 4m^2 +4mn-n^2
b ) ( a+b+c)^2 + (a+b+c )^2 - 4c^2
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9 tháng 8 2016
a) x2 - 2xy + y2 - 4m2 + 4mn - n2 = (x - y)2 - [(2m)2 - 2.2m.n + n2] = (x - y)2 - (2m - n)2
= [(x - y) - (2m - n)][(x - y) + (2m - n)] = (x - y - 2m + n)(x - y + 2m - n)
b) x2 - 4x2y2 + y2 + 2xy = x2 + 2xy + y2 - 4x2y2 = (x + y)2 - (2xy)2 = (x + y - 2xy)(x + y + 2xy)
c) x6 - y6 = (x3)2 - (y3)2 = (x3 - y3)(x3 + y3) = (x - y)(x2 + xy + y2)(x + y)(x2 - xy - y2)
d) 25 - a2 + 2ab - b2 = 25 - (a2 - 2ab + b2) = 52 - (a - b)2 = (5 - a + b)(5 + a - b)
25 tháng 7 2021
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: \(9\left(x+y-1\right)^2-4\left(2x+3y+1\right)^2\)
\(=\left(3x+3y-3\right)^2-\left(4x+6y+2\right)^2\)
\(=\left(3x+3y-3-4x-6y-2\right)\left(3x+3y-3+4x+6y+2\right)\)
\(=-\left(x+3y+5\right)\left(7x+9y-1\right)\)
25 tháng 7 2021
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: \(x^2-2xy+y^2-4m^2+4mn-n^2\)
\(=\left(x^2-2xy+y^2\right)-\left(4m^2-4mn+n^2\right)\)
\(=\left(x-y\right)^2-\left(2m-n\right)^2\)
\(=\left(x-y-2m+n\right)\left(x-y+2m-n\right)\)
2 tháng 10 2020
a) ( 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 )
b) 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 )
c) -4x2 + 12xy - 9y2 + 25
= 25 - ( 4x2 - 12xy + 9y2 )
= 52 - ( 2x - 3y )2
= [ 5 - ( 2x - 3y ) ][ 5 + ( 2x - 3y ) ]
= ( 5 - 2x + 3y )( 5 + 2x - 3y )
d) 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 ) ]
= ( x - y - 2m + n )( x - y + 2m - n )
29 tháng 6 2017
a) (a+b+c)^2 + (a+b-c)^2 - 4c^2
\(=\left(a+b+c\right)^2+\left[\left(a+b-c\right)^2-\left(2c\right)^2\right]\)
\(=\left(a+b+c\right)^2+\left(a+b-c+2c\right)\left(a+b-c-2c\right)\)
\(=\left(a+b+c\right)^2+\left(a+b+c\right)\left(a+b-3c\right)\)
\(=\left(a+b+c\right)\left(a+b+c+a+b-3c\right)\)
\(=\left(a+b+c\right)\left(2a+2b-2c\right)\)
\(=2\left(a+b+c\right)\left(a+b-c\right)\)
b) 4a^2b^2 - (a^2+b^2-c^2)^2
\(=\left(2ab\right)^2-\left(a^2+b^2-c^2\right)^2=\left(2ab+a^2+b^2-c^2\right)\left(2ab-a^2-b^2+c^2\right)\)
\(=\left[\left(a^2+2ab+b^2\right)-c^2\right]\left[c^2-\left(a^2-2ab+b^2\right)\right]\)
\(=\left[\left(a+b\right)^2-c^2\right]\left[c^2-\left(a-b\right)^2\right]\)
\(=\left(a+b+c\right)\left(a+b-c\right)\left(c+a-b\right)\left(c-a+b\right)\)
c) a(b^3-c^3) + b(c^3-a^3) + c(a^3-b^3)
\(=ab^3-ac^3+bc^3-a^3b+a^3c-b^3c\)
\(=a^3\left(c-b\right)+bc\left(c-b\right)\left(c+b\right)-a\left(c-b\right)\left(c^2+bc+b^2\right)\)
\(=a^3\left(c-b\right)+\left(c-b\right)\left(bc^2+b^2c\right)-\left(c-b\right)\left(ac^2+abc+ab^2\right)\)
\(=\left(c-b\right)\left(a^3+bc^2+b^2c-ac^2-abc-ab^2\right)\)
29 tháng 6 2017
a) (a+b+c)^2 + (a+b-c)^2 - 4c^2
\(=\left(a+b+c\right)^2+\left[\left(a+b-c\right)^2-\left(2c\right)^2\right]\)
\(=\left(a+b+c\right)^2+\left(a+b-c+2c\right)\left(a+b-c-2c\right)\)
\(=\left(a+b+c\right)^2+\left(a+b+c\right)\left(a+b-3c\right)\)
\(=\left(a+b+c\right)\left(a+b+c+a+b-3c\right)\)
\(=\left(a+b+c\right)\left(2a+2b-2c\right)\)
\(=2\left(a+b+c\right)\left(a+b-c\right)\)
b) 4a^2b^2 - (a^2+b^2-c^2)^2
\(=\left(2ab\right)^2-\left(a^2+b^2-c^2\right)^2=\left(2ab+a^2+b^2-c^2\right)\left(2ab-a^2-b^2+c^2\right)\)
\(=\left[\left(a^2+2ab+b^2\right)-c^2\right]\left[c^2-\left(a^2-2ab+b^2\right)\right]\)
\(=\left[\left(a+b\right)^2-c^2\right]\left[c^2-\left(a-b\right)^2\right]\)
\(=\left(a+b+c\right)\left(a+b-c\right)\left(c+a-b\right)\left(c-a+b\right)\)
c) a(b^3-c^3) + b(c^3-a^3) + c(a^3-b^3)
\(=ab^3-ac^3+bc^3-a^3b+a^3c-b^3c\)
\(=a^3\left(c-b\right)+bc\left(c-b\right)\left(c+b\right)-a\left(c-b\right)\left(c^2+bc+b^2\right)\)
\(=a^3\left(c-b\right)+\left(c-b\right)\left(bc^2+b^2c\right)-\left(c-b\right)\left(ac^2+abc+ab^2\right)\)
\(=\left(c-b\right)\left(a^3+bc^2+b^2c-ac^2-abc-ab^2\right)\)
NT
0
1 tháng 1 2022
`a. =4(x^2+4x+3)=4(x^2+3x+x+3)=4(x+3)(x+1)`
`b. =x^2+8x-7x-56=x(x+8)-7(x+8)=(x+8)(x-7)`
`c. =x^2-9x+8x-72=x(x-9)+8(x-9)=(x-9)(x+8)`
`d. =(x-y)^2-9=(x-y-3)(x-y+3)`
a) = (x^2-2xy+y^2)-(4m^2-4mn+n^2)
=(x+y)^2-(2-n)^2
=(x+y-2+n)(x+y+2-n)
B) c/m tương tự nhé!
a)x2-2xy+y2-4m2+4mn-n2=(x2-2xy+y2)-((2m)2-4mn+n2)=(x-y)2-(2m-n)2=(x-y+2m-n)(x-y-2m+n)
b)(a+b+c)2+(a+b+c)2-4c2=(a+b+c)+(a+b+c)2-(2c)2=(a+b+c)2+(a+b+c+2c)(a+b+c-2c)=(a+b+c)2+(a+b+3c)(a+b-c)=(a+b-c)(a+b-c+a+b+3c)=(a+b-c)(2a+2b+2c)=2(a+b-c)(a+b+c)