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a) a2 + b2 - c2 - d2 - 2ab + 2cd
b) x2 (y - z)+ y2 (z - x)+ z2 (x - y)
a.= \(\left(a^2-2ab+b^2\right)-\left(c^2-2cd+d^2\right)\)
=\(\left(a-b\right)^2-\left(c-d\right)^2\)
a) x3 + x2y - x2z - xyz
= ( x3 + x2y ) - ( x2z + xyz )
= x2( x + y ) + xz( x + y )
= ( x + y )( x2 + xz )
= x( x + y )( x + z )
b) x2 - y2 + 6x + 9
= ( x2 + 6x + 9 ) - y2
= ( x + 3 )2 - y2
= ( x - y + 3 )( x + y + 3 )
c) x2 - 4xy - x + 2y + 4y2
= ( x2 - 4xy + 4y2 ) - ( x - 2y )
= ( x - 2y )2 - ( x - 2y )
= ( x - 2y )( x - 2y - 1 )
d) 18x3 - 12x2 + 3x - 2
= ( 18x3 - 12x2 ) + ( 3x - 2 )
= 6x2( 3x - 2 ) + ( 3x - 2 )
= ( 3x - 2 )( 6x2 + 1 )
e) a2 + 2ab + b2 - c2 + 2cd - d2
= ( a2 + 2ab + b2 ) - ( c2 - 2cd + d2 )
= ( a + b )2 - ( c - d )2
= ( a + b - c + d )( a + b + c - d )
f) xz - yz - x2 + 2xy - y2
= z( x - y ) - ( x2 - 2xy + y2 )
= z( x - y ) - ( x - y )2
= ( x - y )( z - x + y )
a) x3 + x2y - x2z - xyz
= ( x3 + x2y ) - ( x2z + xyz )
= x2( x + y ) + xz( x + y )
= ( x + y )( x2 + xz )
= x( x + y )( x + z )
b) x2 - y2 + 6x + 9
= ( x2 + 6x + 9 ) - y2
= ( x + 3 )2 - y2
= ( x - y + 3 )( x + y + 3 )
c) x2 - 4xy - x + 2y + 4y2
= ( x2 - 4xy + 4y2 ) - ( x - 2y )
= ( x - 2y )2 - ( x - 2y )
= ( x - 2y )( x - 2y - 1 )
d) 18x3 - 12x2 + 3x - 2
= ( 18x3 - 12x2 ) + ( 3x - 2 )
= 6x2( 3x - 2 ) + ( 3x - 2 )
= ( 3x - 2 )( 6x2 + 1 )
e) a2 + 2ab + b2 - c2 + 2cd - d2
= ( a2 + 2ab + b2 ) - ( c2 - 2cd + d2 )
= ( a + b )2 - ( c - d )2
= ( a + b - c + d )( a + b + c - d )
f) xz - yz - x2 + 2xy - y2
= z( x - y ) - ( x2 - 2xy + y2 )
= z( x - y ) - ( x - y )2
= ( x - y )( z - x + y )
a) \(x^2-2x+1-y^2=\left(x-1\right)^2-y^2=\left(x-1-y\right)\left(x-1+y\right)\)
b)\(=\left(x+y\right)^2-z^2=\left(x+y+z\right)\left(x+y-z\right)\)
mấy ý còn lại tương tự nha
a,\(x^2-y^2+1-2x\)
\(=\left(x-1\right)^2-y^2\)
\(=\left(x-1+y\right)\left(x-1-y\right)\)
\(b,x^2+2xy-z^2+y^2\)
\(=\left(x+y\right)^2-z^2\)
\(=\left(x+y+z\right)\left(x+y-z\right)\)
a) \(x^3+2x^2+3x+2=x^3+x^2+x^2+x+2x+2=x^2\left(x+1\right)+x\left(x+1\right)+2\left(x+1\right)\)
\(=\left(x+1\right)\left(x^2+x+2\right)\)
b) \(=\left(x-y\right)^2-\left(a-b\right)^2=\left(x-y+a-b\right)\left(x-y-a+b\right)\)
a) x3+2x2+3x+2
= x3+x2+x2+x+2x+2
= x2(x+1)+x(x+1)+2(x+1)
= (x+1)(x2+x+2)
b) x2-2xy+y2-a2+2ab-b2
= (x2-2xy+y2)-(a2-2ab+b2)
= (x-y)2-(a-b)2
= (x-y+a-b)(x-y-a+b)
d,=(2bc+b2+c2−a2)(2bc−b2−c2+a2)
=[(b+c)2−a2][−(b+c)2+a2]
=(b+c−a)(b+c+a)2(a−b−c)
\(a^2-b^2+4bc-4c^2\)
\(=a^2-\left(b^2-4bc+4c^2\right)\)
\(=a^2-\left(b-2c\right)^2\)
\(=\left(a-b+2c\right)\left(a+b-2c\right)\)