解题思路:根据整式的运算顺序,先算乘除,后算加减,有括号先算括号里面的,乘法运算时,系数与系数相乘,相同字母与相同字母相乘,底数不变指数相加,再根据整式除法法则,系数与系数相除,相同字母与相同字母相除,底数不变指数相减,能用完全公式或平方差公式的可运用公式,可减小计算量,分别得出结果即可.
(1)(-3a)3-(-a)•(-3a)2,
=-27a3+a×9a2,
=-18a3;
(2)4-(-2)-2-32÷(3.14-π)0,
=4-[1
(−2) 2-9×1,
=-
21/4];
(3)-0.2514×230,
=-([1/4])14×230,
=-2-28×230,
=-4;
(4)1982=(200-2)2,
=2002-2×200×2+22,
=40000-800+4,
=39204;
(5)(-2x) 2•(-0.5xy3),
=4x2•(-[1/2]xy3),
=-2x3y3;
(6)(3x2y-2x+1)(-2xy),
=3x2y•(-2xy)+(-2x)•(-2xy)+1•(-2xy),
=-6x3y2+4x2y-2xy;
(7)(-4x-y)(4x-y),
=(-y-4x)(-y+4x),
=(-y)2-(4x)2,
=y2-16x2;
(8)-3a(a-b)2,
=-3a(a2-2ab+b2),
=-3a•a2-(-3a)•2ab+(-3a)•b2,
=-3a3+6a2b-3ab2;
(9)(a+2b-3c)(a-2b-3c),
=(a-3c+2b)(a-3c-2b),
=(a-3c)2-(2b)2,
=(a2-6ac+9c2)-4b2,
=a2-6ac+9c2-4b2;
(10)(2a+b)2(2a-b)2,
=[(2a+b)(2a-b)]2,
=[(2a)2-b2]2,
=(4a2-b2)2,
=16a4-8a2b2+b4.
点评:
本题考点: 整式的混合运算.
考点点评: 此题主要考查了整式的混合运算,以及运用公式进行整式运算,题难度不大,关键是注意运算的顺序以及符号问题.