Question

分解因式 4a^3-16a^2b+16ab^2 （a+b)^2-4ab (x-y)^2-4(x-y-1)

Answer 1

4a^3-16a^2b+16ab^2
= 4a(a^2-4ab+4b^2)
= 4a(a-2b)^2

(a+b)^2-4ab
=a^2+2ab+b^2-4ab
=a^2-2ab+b^2
=(a-b)^2

(x-y)^2-4(x-y-1)
= (x-y)^2-4(x-y) +4
= (x-y-2)^2

Answer 2

解：4a³-16a²b+16ab²
=4a(a²-4ab+4b²)
=4a(a-2b)²
(a+b)²-4ab
=a²+b²+2ab-4ab
=a²-2ab+b²
=(a-b)²
(x-y)²-4(x-y-1)
=(x-y)²-4(x-y)+4
=(x-y)²-2×(x-y)×2+2²
=(x-y-2)²