Question

整式的除法

利用乘法公式计算：
(a^2-b^2)除以(a+b)
[(a+b)^2-4ab]除以(a-b)^2
(a^4-b^4)除以（a^2+b^2)除以(a+b)

Answer 1

解：(a²-b²)÷(a+b)
=[(a+b)(a-b)]÷(a+b)
=a-b

a^2-b^2)除以(a+b)
[(a+b)^2-4ab]除以(a-b)^2
(a^4-b^4)除以（a^2+b^2)除以(a+b) [(a+b)²-4ab]÷(a-b)²
=(a²+2ab+b²-4ab)÷(a-b)²
=(a²-2ab+b²)÷(a-b)²
=(a-b)²÷(a-b)²
=1
(a^4-b^4)÷(a²+b²)÷(a+b)
=[(a²+b²)(a²-b²)÷[(a²+b²)(a+b)]
=[(a²+b²)(a+b)(a-b)]÷[(a²+b²)(a+b)]
=a-b
a^4-b^4)÷(a²+b²)÷(a+b)
=[(a²+b²)(a²-b²)÷[(a²+b²)(a+b)]
=[(a²+b²)(a+b)(a-b)]÷[(a²+b²)(a+b)]
=a-b

Answer 2

解：(a²-b²)÷(a+b)
=[(a+b)(a-b)]÷(a+b)
=a-b

[(a+b)²-4ab]÷(a-b)²
=(a²+2ab+b²-4ab)÷(a-b)²
=(a²-2ab+b²)÷(a-b)²
=(a-b)²÷(a-b)²
=1

(a^4-b^4)÷(a²+b²)÷(a+b)
=[(a²+b²)(a²-b²)÷[(a²+b²)(a+b)]
=[(a²+b²)(a+b)(a-b)]÷[(a²+b²)(a+b)]
=a-b

Answer 3

a^2-b^2)除以(a+b)
[(a+b)^2-4ab]除以(a-b)^2
(a^4-b^4)除以（a^2+b^2)除以(a+b)