计算： $(1)(a^{2})^{3}\cdot(a^{2}-2ab+1);(2)6x(-x^{2}-xy+y^{2})(-xy);(3)2x^{2}y(3-x^{4}y)-(5x^{3}y)^{2};(4)x^{2}(x-1)-x(x^{2}+x-1);(5)(-2xy^{2})^{2}\cdot(\dfrac{1}{4}y^{2}-\dfrac{1}{2}x^{2}-\dfrac{3}{2}xy);(6)3a(2a^{2}-4a+3)-2a^{2}(3a-4).$

1. 运用幂的乘方法则化简前面的单项式

$(a^{2})^{3}\cdot(a^{2}-2ab+1) = a^{6}(a^{2}-2ab+1)$

2. 运用单项式乘多项式法则展开式子

$a^{6}\cdot a^{2} - a^{6}\cdot 2ab + a^{6}\cdot 1 = a^{8}-2a^{7}b+a^{6}$

1. 先计算单项式相乘，简化系数和字母部分

$6x(-x^{2}-xy+y^{2})(-xy) = [6x\cdot(-xy)]\cdot(-x^{2}-xy+y^{2}) = -6x^{2}y(-x^{2}-xy+y^{2})$

2. 展开单项式与多项式的乘积

$-6x^{2}y(-x^{2}) - 6x^{2}y(-xy) + (-6x^{2}y)(y^{2}) = 6x^{4}y+6x^{3}y^{2}-6x^{2}y^{3}$

1. 展开前一项的单项式乘多项式及后一项的积的乘方

$2x^{2}y(3-x^{4}y) = 6x^{2}y - 2x^{6}y^{2}$
$(5x^{3}y)^{2} = 25x^{6}y^{2}$

2. 合并同类项得出最简结果

$(6x^{2}y - 2x^{6}y^{2}) - 25x^{6}y^{2} = 6x^{2}y - 27x^{6}y^{2}$

1. 分别展开两组乘积

$x^{2}(x-1) - x(x^{2}+x-1) = (x^{3}-x^{2}) - (x^{3}+x^{2}-x)$

2. 去括号并合并同类项

$x^{3}-x^{2}-x^{3}-x^{2}+x = -2x^{2}+x$

1. 计算积的乘方

$(-2xy^{2})^{2} = 4x^{2}y^{4}$

2. 运用单项式乘多项式法则展开各分项

1. 展开两组乘积

$3a(2a^{2}-4a+3) - 2a^{2}(3a-4) = (6a^{3}-12a^{2}+9a) - (6a^{3}-8a^{2})$

2. 去括号并合并同类项

$6a^{3}-12a^{2}+9a-6a^{3}+8a^{2} = -4a^{2}+9a$