因式分解:9-x^2-6x+9y^2 x^2+8xy+16y^2+3x+3y+21:9-x^2-6x+9y^2 2:x^2+8xy+16y^2+3x+3y+2
问题描述:
因式分解:9-x^2-6x+9y^2 x^2+8xy+16y^2+3x+3y+2
1:9-x^2-6x+9y^2
2:x^2+8xy+16y^2+3x+3y+2
答
1. 9-x^2-6x+9y^2
=-(x^2+6x-9-9y^2)
=-[(x-3)^2-(3y)^2]
=-(x-3+3y)(x-3-3y)
2:x^2+8xy+16y^2+3x+12y+2
=(x^2+8xy+16y^2)+(3x+12y)+2
=(x+4y)^2+3(x+4y)+2
=(x+4y+1)(x+4y+2)对不起,第二题我也不会,题是不是错了
答
1. 9-x^2-6x+9y^2
=(9y^2-x^2)+(9-6x)
=(3y+x) (3y-x)+3(3-2x)
2:x^2+8xy+16y^2+3x+3y+2
=(x^2+8xy+16y^2)+(3x+3y)+2
=(x+4y)^2+3(x+y)+2
答
1:9-x^2-6x+9y^2
=9+9y^2-x^2-6x
=9(1+y^2)-(x^2+6x)
=9(y^2+1)-x(x+6)
2:x^2+8xy+16y^2+3x+3y+2
=x^2+2*x*4y+(4y)^2+3x+3y+2
=(x+4y)^2+3x+3y+2
=(x+4y)^2+3(x+y)+2