Question

因式分解：（1）：a^3-12a^2b+36ab^2（2）：（x+y）^2+4(x-y)^2-4(x^2-y^2) (3):(x^2-2x-2)(x^2-2x+4)+9

（4）：-14abc-7ab+49ab^2c (5):25(m+n)^2-4(m-n)^2
5.已知mn^2=-2 求多项式-mn(m^2n^5-mn^3-n)

Answer 1

a^3-12a^2 b+36ab^2

=a^3-6a^2 b-6a^2 b+36ab^2

〖=a〗^2 (a-6b)-6ab(a-6b)

=(a-6b)(a^2-6ab)

〖（x+y）〗^2+4〖(x-y)〗^2-4(x^2-y^2) 

=x^2+2xy+y^2+4x^2-8xy+4y^2-4x^2+4y^2

=x^2-6xy+9y^2

=(x-3y)^2

(x^2-2x-2)(x^2-2x+4)+9

=(x^2-2x)^2+2(x^2-2x)+1

=[(x^2-2x)+1]^2

=(x^2-2x+1)^2

=(x-1)^4

-14abc-7ab+49ab^2 c

=-7ab(2c-7bc)-7ab

=-7ab(2c-7bc+1)

=-7ab[c(2-7b)+1]

25〖(m+n)〗^2-4〖(m-n)〗^2

=25(m^2+2mn+n^2 )-4(m^2-2mn+n^2 )

=21m^2+58mn+21n^2

=(7m+3n)(3m+7n)

已知mn^2=-2 求多项式-mn(m^2 n^5-mn^3-n) 

-mn(m^2 n^5-mn^3-n)

=mn^2 (-mn)(mn^3-n-n)

=mn^2 (-m^2 n^4+mn^2+mn^2)

以mn^2=-2代入

=(-2)[(-(-2)^2+(-2)+(-2))]

=(-2)(-8)=16