bn nào lm giúp mik câu này vs ạ x³+y³+z³-3xyz 05/08/2021 Bởi Charlie bn nào lm giúp mik câu này vs ạ x³+y³+z³-3xyz
Đáp án: `(x + y + z)(x² + y² + z² – xy – yz – zx)` Giải thích các bước giải: `x³ + y³ + 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 + z)(x + y)z – 3xy(x + y + z)` `= (x + y + z)³ – 3(x + y + z)(xy + yz + zx)` `= (x + y + z)[(x + y + z)² – 3xy – 3yz – 3zx)]` `= (x + y + z)(x² + y² + z² – xy – yz – zx)` Bình luận
x³+y³+z³-3xyz =(x+y)³-3xy(x-y)+z³-3xyz =[(x+y)³+z³]-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]ư =(x+y+z)(x²+y²+z²+2xy+2xz+2yz-3xz-3yz-3xy) =(x+y+z)(x²+y²+z²-xy-xz-yz) Bình luận
Đáp án:
`(x + y + z)(x² + y² + z² – xy – yz – zx)`
Giải thích các bước giải:
`x³ + y³ + 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 + z)(x + y)z – 3xy(x + y + z)`
`= (x + y + z)³ – 3(x + y + z)(xy + yz + zx)`
`= (x + y + z)[(x + y + z)² – 3xy – 3yz – 3zx)]`
`= (x + y + z)(x² + y² + z² – xy – yz – zx)`
x³+y³+z³-3xyz
=(x+y)³-3xy(x-y)+z³-3xyz
=[(x+y)³+z³]-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]ư
=(x+y+z)(x²+y²+z²+2xy+2xz+2yz-3xz-3yz-3xy)
=(x+y+z)(x²+y²+z²-xy-xz-yz)