因式分解,(1)(x^2+1)y^2-x^2-1 (2)a-ab^2 (3)2a^4+4a^3+2a^2 (4)a^2(a-1)-4(1-a)^2
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![因式分解,(1)(x^2+1)y^2-x^2-1 (2)a-ab^2 (3)2a^4+4a^3+2a^2 (4)a^2(a-1)-4(1-a)^2](/uploads/image/z/1246916-20-6.jpg?t=%E5%9B%A0%E5%BC%8F%E5%88%86%E8%A7%A3%2C%EF%BC%881%EF%BC%89%EF%BC%88x%5E2%2B1%29y%5E2-x%5E2-1+%282%29a-ab%5E2+%283%292a%5E4%2B4a%5E3%2B2a%5E2+%284%29a%5E2%28a-1%29-4%281-a%29%5E2)
因式分解,(1)(x^2+1)y^2-x^2-1 (2)a-ab^2 (3)2a^4+4a^3+2a^2 (4)a^2(a-1)-4(1-a)^2
因式分解,(1)(x^2+1)y^2-x^2-1 (2)a-ab^2 (3)2a^4+4a^3+2a^2 (4)a^2(a-1)-4(1-a)^2
因式分解,(1)(x^2+1)y^2-x^2-1 (2)a-ab^2 (3)2a^4+4a^3+2a^2 (4)a^2(a-1)-4(1-a)^2
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(1)(x^2+1)y^2-x^2-1
=(x²+1)(y²-1)
=(x²+1)(y+1)(y-1)
(2)a-ab^2
=a(1-b²)
=a(1+b)(1-b)
(3)2a^4+4a^3+2a^2
=2a²(a²+2a+1)
=2a²(a+1)²
(4)a^2(a-1)-4(1-a)^2
=(a-1)(a²-4a+4)
=(a-1)(a-2)²
(1)(x^2+1)y^2-x^2-1
=x²y²+y²-x²-1
=x²y²-1
=(xy-1)(xy+1)
(2)a-ab^2
=a(1-b²)
=a(1-b)(1+b)
(3)2a^4+4a^3+2a^2
=2a²(a²+2a+1)
=2a²(a+1)²
(4)a^2(a-1)-4(1-a)^2
=(a-1)(a²-4a+4)
=(a-1)(a-2)²
1)(x^2+1)y^2-x^2-1
=(x²+1)(y+1)(y-1)
(2)a-ab^2
=a(1-b²)
=a(1+b)(1-b)
(3)2a^4+4a^3+2a^2
=2a²(a²+2a+1)
=2a²(a+1)²
(4)a^2(a-1)-4(1-a)^2
=(a-1)(a²-4a+4)
=(a-1)(a-2)²
(1)(x^2+1)y^2-x^2-1
=x^2y^2+y^2-x^2-1
=x^2(y^2-1)+y^2-1
=(x^2+1)(y^2-1)
=(x^2+1)(y-1)(y+1)
(2)a(1-b)(1+b)
(3)2a^4+4a^3+2a^2
=2a^4+2a^3+2a^3+2a^2
=2a^3(a+1)+2a^2(a+1)
=(2a^3+2a^2)(a+1)
=2a^2(a+1)^2
(4)a^2(a-1)-4(1-a)^2
=(a-1)(a^2-4a+4)
=(a-1)(a-2)^2