Đáp án+Giải thích các bước giải:
Bài toán `6:`
`a) x^2-4x^2y^2+y^2+2xy`
`=(x^2+2xy+y^2)-4x^2y^2`
`=(x+y)^2-(2xy)^2`
`=(x+2xy+y).(x-2xy+y)`
`b) x^6-y^6`
`=(x^3)^2-(y^3)^2`
`=(x^3-y^3).(x^3+y^3)`
`=(x-y)(x^2+xy+y^2)(x+y)(x^2-xy+y^2)`
`c) 25-x^2+2xy-y^2`
`=25-(x^2-2xy+y^2)`
`=5^2-(x-y)^2`
`=(5-x+y)(5+x-y)`
`d) 4b^2c^2-(b^2+c^2-a^2)->`Sửa đề:`4b^2c^2-(b^2+c^2-a^2)^2`
`4b^2c^2-(b^2+c^2-a^2)^2`
`=(2bc)^2-(b^2+c^2-a^2)^2`
`=(2bc-b^2-c^2+a^2)(2bc+b^2+c^2-a^2)`
`=-(b^2-2ab+c^2-a^2)(b^2+2bc+c^2-a^2)`
`=-[(b-c)^2-a^2][(b+c)^2-a^2]`
`=-(b-c-a)(b-c+a)(b+c-a)(b+c+a)`
`e) (x+y+z)^2+(x+y-z)^2-4z^2`
`=[(x+y)+z]^2+[(x+y)-z]^2-4z^2`
`=(x+y)^2+2(x+y).z+z^2+(x+y)^2-2(x+y).z+z^2-4z^2`
`=2(x+y)^2-2z^2`
`=2[(x+y)^2-z^2]`
`=2(x+y-z)(x+y+z)`
`g) 9(x+y-1)^2-4(2x+3y+1)^2`
`=(3x+3y-3)^2-(4x+6y+2)^2`
`=[(3x+3y-3)-(4x+6y+2)][(3x+3y-3)+(4x+6y+2)]`
`=(3x+3y-3-4x-6y-2)(3x+3y-3+4x+6y+2)`
`=-(x+3y+5)(7x+9y-1)`
