分解因式：①3a-12a^2+18a^3②(x+y)^2(x-y)-(x+y)(x-y)^2③18-2x^4④-0.49b^2+25a^2
问题描述：
分解因式：①3a-12a^2+18a^3②(x+y)^2(x-y)-(x+y)(x-y)^2③18-2x^4④-0.49b^2+25a^2
答
①3a-12a^2+18a^3
=3a(1-4a+6a²)
②(x+y)^2(x-y)-(x+y)(x-y)^2
=(x+y)(x-y)(x+y-x+y)
=2y(x+y)(x-y)
③18-2x^4
=2(9-x^4)
=2(3+x²)(3-x²)
④-0.49b^2+25a^2
=(5a+0.7b)(5a-0.7b)
答
①3a-12a^2+18a^3
=3a(1-4a+6a^2)
②(x+y)^2(x-y)-(x+y)(x-y)^2
=(x+y)(x-y)[(x+y)-(x-y)]
=(x+y)(x-y)(x+y-x+y)
=2y(x+y)(x-y)
③18-2x^4
=2(9-x^4)
=2(3-x^2)(3+x^2)
④-0.49b^2+25a^2
=(5a-0.7b)(5a+0.7b)