Đáp án+Giải thích các bước giải:
Bài 55:
`1) (x^2-9y^2)-(4x+12y)`
`=(x-3y)(x+3y)-4(x+3y)`
`=(x+3y)(x-3y-4)`
`2)(x^2-16y^2)-3x+12y`
`=(x-4y)(x+4y)-3(x-4y)`
`=(x-4y)(x+4y-3)`
`3) -x^2+2xy-y^2+25`
`=-(x^2-2xy+y^2-25)`
`=-[(x^2-2xy+y^2)-25]`
`=-[(x-y)^2-5^2]`
`=-(x-y-5)(x-y+5)`
`4) x^3+6x^2+12x+8`
`= x^3+3.x^2 . 2+3.x.2^2 + 2^3`
`=(x+2)^3`
`5) x^3-6x^2+9x`
`=x(x^2-6x+9)`
`=x(x-3)^2`
`6) x^4-4x^3-8x^2+8x`
`=x(x^3-4x^2-8x+8)`
`=x(x^3+2x^2-6x^2-12x+4x+8)`
`=x[x^2(x+2)-6x(x+2)+4(x+2)]`
`=x(x+2)(x^2-6x+4)`
`7) x^3-x^2y-xy^2+y^3`
`=x^2(x-y)-y^2(x-y)`
`=(x^2-y^2)(x-y)`
`=(x-y)(x+y)(x-y)`
`=(x-y)^2(x+y)`
`8) x^4+2x^3+x^2-y^2`
`=(x^4+2x^3+x^2)-y^2`
`=(x^2+x)^2-y^2`
`=(x^2+x-y)(x^2+x+y)`
`9) 9(x-1)^2-4(2x+3)^2`
`=3^2 . (x-1)^2-2^2 . (2x+3)^2`
`=[3(x-1)]^2-[2(2x+3)]^2`
`=[(3x-3)-(4x+6)][(3x-3)+(4x+6)]`
`=(3x-3-4x-6)(3x-3+4x+6)`
`=(-x-9)(7x+3)`
`10) 4x^2(x+y)-x-y`
`=4x^2(x+y)-(x+y)`
`=(4x^2-1)(x+y)`
`=(2x-1)(2x+1)(x+y)`
