3) \(x^2-6x+5\)
\(=x^2-x-5x+5\)
\(=\left(x^2-x\right)-\left(5x-5\right)\)
\(=x\left(x-1\right)-5\left(x-1\right)\)
\(=\left(x-1\right)\left(x-5\right)\)
4) \(x^4+64\)
\(=x^4+16x^2+64-16x^2\)
\(=\left[\left(x^2\right)^2+2.x^2.8+8^2\right]-16x^2\)
\(=\left(x^2+8\right)^2-16x^2\)
\(=\left(x^2+8-16x\right)\left(x^2+8+16x\right)\)
1) \(\left(x-y\right)^3+\left(y-z\right)^3+\left(z-x\right)^3\)
\(=\left(x^3-3x^2y+3xy^2-y^3\right)+\left(y^3-3y^2z+3yz^2-z^3\right)+\left(z^3-3z^2x+3zx^2-x^3\right)\)
\(=x^3-3x^2y+3xy^2-y^3+y^3-3y^2z+3yz^2-z^3+z^3-3z^2x+3zx^2-x^3\)
\(=-3x^2y+3xy^2-3y^2z+3yz^2-3z^2x+3zx^2\)
\(=-3\left(x^2y-xy^2+y^2z-yz^2+z^2x-zx^2\right)\)
2. a2( b - c ) + b2 ( c - a ) + c2 ( a - b )
= (a2b-a2c+b2c-b2a)+c2(a-b)
= (a2b-b2a)-(a2c-b2c)-c2(a-b)
= ab(a-b)-c(a2-b2)-c2(a-b)
= ab(a-b)-c(a-b)(a+b)-c2(a-b)
= (a-b)(ab-c(a+b)-c2)
= (a-b)(ab-ca-cb-c2)
=(a-b)[(ab-ac)+(-cb-c2)]
= (a-b)[a(b-c)-c(b-c)]
= (a-b)(b-c)(a-c)
2. a2( b - c ) + b2 ( c - a ) + c2 ( a - b)
= a2b-a2c+b2c-b2a+c2(a-b)
=(a2b-b2a)-(a2c-b2c)+c2(a-b)
= ab(a-b)-c(a2-b2)+c2(a-b)
=ab(a-b)-c(a-b)(a+b)+c2(a-b)
=(a-b)(ab-c(a+b)+c2)
= (a-b)[ab-ca-cb+c2]
= (a-b)[(ab-ca)-(cb-c2)]
= (a-b)[ a(b-c)-c(b-c)]
= (a-b)(b-c)(a-c)
1 . Cứ tách hằng đẳng thức rồi rút gọn là ra , dài lắm , tớ lười
2 . a2( b - c ) + b2 ( c - a ) + c2 ( a - b )
= a2b - a2c + b2c - ab2 + c2 ( a - b )
= ab( a - b) - c( a2 - b2 ) + c2 ( a - b )
= ab( a - b) - c( a + b)( a - b) + c2 ( a - b )
= ( a - b)( ab - ac - bc + c2 )
= ( a - b)[ a( b - c) - c( b - c) ]
= ( a - b)( b - c)( a - c)
c) x2 - 6x + 5
= x2 - x - 5x + 5
= x( x - 1) - 5( x - 1)
= ( x - 1)( x - 5)
d) x4 + 64
= ( x2)2 + 2.8x2 + 82 - 16x2
= ( x2 + 8)2 - ( 4x )2
= ( x2 - 4x + 8)( x2 + 4x + 8)
