Question

因式分解 (1)4a^4-64(2)x^4-18x^2y^2+81y^4(3)(x^2-y

^2-(1-y)^2

Answer 1

4a^4-64
=4(a^4-16)
=4(a²-4)(a²+4)
=4(a-2)(a+2)(a²+4)

x^4-18x²y²+81y^4
=(x²-9y²)²
=(x-3y)²(x+3y)²

(x²-y)²-(1-y)²
=(x²-y-1+y)(x²-y+1-y)
=(x²-1)(x²-2y+1)
=(x-1)(x+1)(x²-2y+1)

Answer 2

(1)
4a^4-64
=4(a^4-16)
=4(a^4-2^4)
=4(a^2+2^2)(a^2-2^2)
=4(a^2+2^2)(a+2)(a-2)
=4(a+2)(a-2)(a^2+2^2)

(2)
x^4-18x^2y^2+81y^4
=(x^2-9y^2)^2
=[(x+3y)(x-3y)]^2
=(x+3y)^2(x-3y)^2

(3)
(x^2-y)^2- (1-y)^2
=(x^2-y+1-y)(x^2-y-1+y)
=(x^2-2y+1)(x^2-1)
=(x^2-2y+1)(x+1)(x-1)
=(x+1)(x-1)(x^2-2y+1)