Đáp án:+Giải thích các bước giải:

 `17 . 27xy + xy (x+b)^3`

`=xy[27 + (a+b)^3]`

`=xy [ 3^3 + (a+b)^3]`

`=xy ( 3+a+b)[3^2 -3.(a+b) + (a+b)^2]`

`=xy (3+a+b)(9 - 3a-3b +a^2 + 2ab+b^2)`

`18 . 8xy^3 +x(x-y)^3`

`=x(8y^3 + (x-y)^3)`

`=x[(2y)^3 + (x-y)^3]`

`=x(2y +x-y)[(2y)^2 - 2y(x-y) + (x-y)^2]`

`=x(x+y)(4y^2 - 2xy + 2y^2  +x^2 - 2xy + y^2]`

`=x(x+y)(7y^2 - 4xy + x^2)`

`19 . x^2 - (a+b)xy + aby^2`

`=x^2 - axy - bxy + aby^2`

`=x(x-ay) - by(x-ay)`

`=(x-ay)(x-by).`

`20  x^2 - (2a+b) xy + 2aby^2`

`=x^2 - 2axy - bxy + 2aby^2`

`=x(x-2ay) - by ( x-2ay)`

`=(x-by)(x-2ay)`

`21 . ab ( x^2 +y^2 )+ xy (x^2+b^2)`

`=abx^2 +aby^2 + xya^2+ xyb^2`

`=ax(bx + ay) + by(ay+bx)`

`=(ay +bx)(ax+by)`

`22 . xy (a^2 +b^1) -ab(x^2+y^2)`

`=xya^2 + xyb^2 - abx^2 - aby^2`

`=ax(ay- bx) - by(ay - bx)`

`=(ay-bx)(ax-by)`

`23 . (xy + ab)^2 + (ay - bx)^2`

`=x^2y^2 + 2xyab + a^2b^2 + a^2y^2 + 2abxy + b^2x^2`

`=x^y^2 + a^2 y^2 + a^b^2 + b^2x^2`

`=y^2(x^2+a^2) +b^2(a^2+x^2)`

`=(a^2+x^2)(y^2+b^2) .`