中二數題=====(x^2 - 4x^3 + 5)(x^4 - 2x - 3)

問題) 化簡(x^2 - 4x^3 + 5)(x^4 - 2x - 3)

回答: (x^2 - 4x^3 + 5)(x^4 - 2x - 3)
= (X^2)(X^4) + X^2(-2X) + X^2(-3) - 4X^3(X^4) - 4X^3(-2X) - 4X^3(-3) + 5(X^4) + 5(-2X) + 5
(-3)
= (X^2+4) + (-2X^3) + (-3X^2) - 4X^3+4 - (-8X^4) - (-12X^3) + 5X^4 + (-10X) +(-15)
= X^6 - 2X^3 - 3X^2 - 4X^7 + 8X^4 + 12X^3 + 5X^4 - 10X - 15
= X^6 - 2X^3 - 3X^2 -4X^7 + 8X^4 + 5X^4 +12X^3 - 10X -15
= X^6 - 2X^3 - 3X^2 -4X^7 + 13X^4 + 12X^3 - 10X -15


*****要緊記各項指數定律:
定律1) (X^n)(X^m) = X^n+m 例1: (X^1)(x^2) = X^3 *[X = X^1]
定律2) (X^n) / (X^m) = X^n-m 例2: (x^2) / (x^3) = x^2-3 = x^ -1 = 1/x(以正指數表示)
(x^3) / (x^2) = x^3-2 = x^1 = x
**「X^0 = 1[任何數的"零"次方,它最終的值是"1"」 **
例如: 8^0 = 1
(3x+2y^3-6xy+8y^4)^0 = 1

(x^2 - 4x^3 + 5)(x^4 - 2x - 3)
=x^6-2x^3-3x^2-4x^7+8x^4+12x^3+5x^4-10x-15
= -x^7+x^6+13x^4+10x^3-3x^2-10x-15


Hopes can help u