Question

Thu gọn các biểu thức sau
a) ( x + 1 ). ( x^2 - x + 1 ) - ( x^3 - 1 )
b) ( x - y ) ^2 - ( x + y ) ^2
c) ( x - 2 ). ( x^2 × 2x + 4 ) + ( 1 - x ).( x^2 + x + 1)

Answer 1

a: \(=x^3+1-x^3+1=2\)

b: \(=x^2-2xy+y^2-x^2-2xy-y^2=-4xy\)

c: \(=x^3-8+1-x^3=-7\)

Answer 2

`(a):\  (x+1)(x^{2}-x+1)-(x^{3}-1)`

`=x^{3}+1^{3}-x^{3}+1`

`=2`

`(b):\  (x-y)^{2}-(x+y)^{2}`

`=x^{2}-2xy+y^{2}-(x^{2}+2xy+y^{2})`

`=-4xy`

`(c):\  (x-2)(x^{2}+2x+4)+(1-x)(x^{2}+x+1)`

`=x^{3}-2^{3}+1^{3}-x^{3}`

`=-8+1=-7`