7x-7y+ x^2 -2xy + y^2 a^2 (b-c) + b^2 (c-a) + c^2 (a-b) 3x^2 + 6xy + 3y^2 – 3z^2 (x-y)^3 + (y-z)^3 + (z-x)^3 23/08/2021 Bởi Aubrey 7x-7y+ x^2 -2xy + y^2 a^2 (b-c) + b^2 (c-a) + c^2 (a-b) 3x^2 + 6xy + 3y^2 – 3z^2 (x-y)^3 + (y-z)^3 + (z-x)^3
7x-7y+ x² -2xy + y² = 7( x-y) + (x-y)² = (7 + x-y)( x-y) 3x² + 6xy + 3y² – 3z²= 3( x² + 2xy + y²- z²) = 3[( x+y)² – z²] = 3( x+y-z)(x+y+z) (x-y)³ + (y-z)³+ (z-x)³= ( x-y + y-z)[ ( x-y)² – (x-y)(y-z) + ( y-z)²)] + (z-x)³ = (x-z)( x-y)² – (x-y)(y-z) + ( y-z)²) + (z-x)³ = (x-z)[( x-y)² – (x-y)(y-z) + ( y-z)² + (z-x)²] Bình luận
7x-7y+ x² -2xy + y² = 7( x-y) + (x-y)²
= (7 + x-y)( x-y)
3x² + 6xy + 3y² – 3z²= 3( x² + 2xy + y²- z²)
= 3[( x+y)² – z²]
= 3( x+y-z)(x+y+z)
(x-y)³ + (y-z)³+ (z-x)³= ( x-y + y-z)[ ( x-y)² – (x-y)(y-z) + ( y-z)²)] + (z-x)³
= (x-z)( x-y)² – (x-y)(y-z) + ( y-z)²) + (z-x)³
= (x-z)[( x-y)² – (x-y)(y-z) + ( y-z)² + (z-x)²]