Đáp án:
x³+y³+z³-3xyz = (x+y+z)(x² + y² + z² - xy - xz - yz)
Giải thích các bước giải:
x³+y³+z³-3xyz
= (x³+3x²y+3xy²+y³)-(3x²y-3xy²)+z³-3xyz
= (x+y)³-3xy(x-y)+z³-3xyz
= [(x+y)³+z³] - 3xy(x+y+z)
= (x+y+z)³ - 3(x+y)²z - 3(x+y)z² - 3xy(x+y+z)
= (x+y+z)³ - 3z(x+y)(x+y+z) - 3xy(x+y+z)
= (x+y+z)[(x+y+z)² - 3z(x+y) - 3xy]
= (x+y+z)(x²+y²+ z²+2xy+2xz+2yz-3xz-3yz-3xy)
= (x+y+z)(x² + y² + z² - xy - xz - yz)
