多项式

练习2.5第10部分

问题:9 -验证:

(我)' x³+ y³= (x + y)(x²- xy + y²)'

答:RHS = ' (x + y)(x^2 - xy + y^2 '

' = x^3 - x^2\y + xy^2 + yx^2 - xy^2 + y^3 '

' = x^3 + y^3 ' = LHS证明

(2)' x³+ y³= (x - y)(x²+ xy + y²)'

答:RHS ' = (x - y)(x²+ xy + y²'

' = x^3 + x^2\y + xy^2 - yx^2 - xy^2 - y^3 '

' = x^3 - y^3 ' = LHS证明

问题:10 -分解以下每一项:

(我)27y^3 + 125z^3

答:考虑到;27y^3 + 125z^3

= (3y)^3 + (5z)^3 '

使用恒等式' x^3 + y^3 = (x + y)(x^2 - xy + y^2) '

得到' 27y^3 + 125z^3 '

' = (3y + 5z)[(3y)^2 - 3y\xx5z + (5z)^2] '

' = (3y + 5z)(9y²- 15yz + 25z²)'

(2)64m^3 - 343n^3 '

答:考虑到;64m^3 - 343n^3 '

' = (4m - 7n)[(4m)²+ 4m\xx7n + (7n)²]'

' = (4m - 7n)(16m²+ 28mn + 49n²)'

问题:11 -分解:

27x^3 + y^3 + z^3 - 9xy\z '

答:考虑到;' 27^3 + y^3 + z^3 - 9xy\z '

' = (3x)^3 + y^3 + z^3 - 3xx3xy\z '

使用恒等式' x^3 + y^3 + z^3 - 3xy\z '

' = (x + y + z)(x²+ y²+ z²- xy - yz - xz) '

我们得到:“(3 x + y + z) [3 x ^ 2 + y ^ 2 + z ^ 2 - 3 xy - yz - 3 xz]”

' = (3 x + y + z) (9 x ^ 2 + y ^ 2 + z ^ 3 - 3 xy - yz - 3 xz)”