1. 计算:
(1)$(x - 3)(x + 6)$; (2)$(2x - 3)(2x + 1)$;
(3)$(2x - 1)(3x^{2} + 2x + 1)$; (4)$(x - 40)(-x + 100)$;
(5)$(x + 2y)(x - 3y) + xy$; (6)$(x + 3y)^{2}$;
(7)$4m(m - n) + (5m - n)(m + n)$; (8)$(x - y)(x + 3y) - x(x + 2y)$;
(9)$(a - 2b)(a^{2} + 2ab + 4b^{2})$; (10)$5y^{2} - (y - 2)(3y + 1) - 2(y + 1)(y - 5)$.
答案：1.(1)$x^{2}+3x-18$ (2)$4x^{2}-4x-3$ (3)$6x^{3}+x^{2}-1$(4)$-x^{2}+140x-4000$ (5)$x^{2}-6y^{2}$ (6)$x^{2}+6xy+9y^{2}$(7)$9m^{2}-n^{2}$ (8)$-3y^{2}$ (9)$a^{3}-8b^{3}$(10)$13y+12$
解析：
(1)解：原式$=x^{2}+6x-3x-18=x^{2}+3x-18$
(2)解：原式$=4x^{2}+2x-6x-3=4x^{2}-4x-3$
(3)解：原式$=6x^{3}+4x^{2}+2x-3x^{2}-2x-1=6x^{3}+x^{2}-1$
(4)解：原式$=-x^{2}+100x+40x-4000=-x^{2}+140x-4000$
(5)解：原式$=x^{2}-3xy+2xy-6y^{2}+xy=x^{2}-6y^{2}$
(6)解：原式$=x^{2}+2\cdot x\cdot 3y+(3y)^{2}=x^{2}+6xy+9y^{2}$
(7)解：原式$=4m^{2}-4mn+5m^{2}+5mn-mn-n^{2}=9m^{2}-n^{2}$
(8)解：原式$=x^{2}+3xy-xy-3y^{2}-x^{2}-2xy=-3y^{2}$
(9)解：原式$=a^{3}+2a^{2}b+4ab^{2}-2a^{2}b-4ab^{2}-8b^{3}=a^{3}-8b^{3}$
(10)解：原式$=5y^{2}-(3y^{2}+y-6y-2)-2(y^{2}-5y+y-5)$
$=5y^{2}-3y^{2}+5y+2-2y^{2}+8y+10=13y+12$
2. 解方程:$(x - 3)(x - 2) + 15 = (x - 9)(x + 1)$.
答案：解：$(x - 3)(x - 2) + 15 = (x - 9)(x + 1)$
$x^2 - 2x - 3x + 6 + 15 = x^2 + x - 9x - 9$
$x^2 - 5x + 21 = x^2 - 8x - 9$
$-5x + 21 = -8x - 9$
$-5x + 8x = -9 - 21$
$3x = -30$
$x = -10$
3. 已知多项式$M = x^{2} + 5x - a$,$N = -x + 2$,$P = x^{3} + 3x^{2} + 5$,且$M\cdot N + P的值与x$的取值无关,求字母$a$的值.
答案：解:$M\cdot N+P=(x^{2}+5x-a)(-x+2)+(x^{3}+3x^{2}+5)$$=-x^{3}+2x^{2}-5x^{2}+10x+ax-2a+x^{3}+3x^{2}+5$$=(10+a)x-2a+5$,$\because M\cdot N+P$的值与x的取值无关,$\therefore 10+a=0$,解得$a=-10$.
解析：
解：$M \cdot N + P = (x^{2} + 5x - a)(-x + 2) + (x^{3} + 3x^{2} + 5)$
$= -x^{3} + 2x^{2} - 5x^{2} + 10x + ax - 2a + x^{3} + 3x^{2} + 5$
$= ( -x^{3} + x^{3}) + (2x^{2} - 5x^{2} + 3x^{2}) + (10x + ax) + (-2a + 5)$
$= (10 + a)x - 2a + 5$
因为$M \cdot N + P$的值与$x$的取值无关，所以含$x$项的系数为$0$，即$10 + a = 0$，解得$a = -10$。
故$a$的值为$-10$。
