1. thu gọn a) M=(x+2)^3-(x-1)^3 b) N=(x-3)^3-(x+1)^3 2) cho a+b=8, a.b=15. Tính A=a^3+b^3 . Giup mình với mn
By aikhanh
1. thu gọn a) M=(x+2)^3-(x-1)^3 b) N=(x-3)^3-(x+1)^3 2) cho a+b=8, a.b=15. Tính A=a^3+b^3 . Giup mình với mn
1 . Thu gọn :
a) M= ( x + 2 )³ – ( x – 1 )³
= x³ + 6x² + 12x + 8 – ( x³ – 3x² + 3x – 1 )
= x³ + 6x² + 12x + 8 – x³ + 3x² – 3x + 1
= 9x² + 9x + 9
b) N = ( x – 3 )³ – ( x + 1 )³
= x³ – 9x² + 27x – 27 – ( x³ + 3x² + 3x + 1 )
= x³ – 9x² + 27x – 27 – x³ – 3x² – 3x – 1
= -12x² + 24x – 28
2 .
A = a³ + b³
= ( a + b )( a² – ab + b² )
= ( a + b )[( a² + b² ) – ab ]
= ( a + b )[( a² + b² + 2ab – 2ab ) – ab ]
= ( a + b )[ ( a + b )² – 3ab ]
Thay số vào ta có :
( a + b )[ ( a + b )² – 3ab ]
= 8 . ( 8² – 3 . 15 )
= 152
~CHÚC BẠN HỌC TỐT~
`a)`
` M = (x+2)^3 – (x-1)^3`
` = x^3 + 6x^2 + 12x + 8 – (x^3 – 3x^2 + 3x -1)`
` = x^3 + 6x^2 +12x + 8- x^3 +3x^2 – 3x +1`
`= 9x^2 +9x +9`
` = 9(x^2+x+1)`
`b)`
` N = (x-3)^3 – (x+1)^3`
` = ( x^3 – 9x^2+ 27x – 27) – (x^3 + 3x^2 +3x +1)`
` = x^3 -9x^2 +27x – 27 – x^3 -3x^2 -3x -1`
` = -12x^2 + 24x- 28`
`2)`
` A = a^3 +b^3 = (a+b)(a^2 – ab +b^2) = 8(a^2 – ab + b^2)`
` = 8 ( a^2 + 2ab + b^2 – 3ab)`
` = 8 [ (a+b)^2 – 3ab]`
` = 8 . ( 8^2 – 3 .15)`
` = 152`