Đáp án:
`a.`
`(5x-2y)(x^2-xy+1)`
`=5x^3-5x^2 y+5x-2x^2 y+2xy^2-2y`
`=5x^3-(5x^2 y+2x^2 y)+2xy^2+5x-2y`
`=5x^3-7x^2 y+2xy^2+5x-2y`
`b.`
`(x-1).(x+1).(x+2)`
`=(x^2-1).(x+2)`
`=x^3+2x^2-x-2`
`c.`
`(1)/(2).x^{2}.y^{2}.(2x+y).(2x-y)`
`=(1)/(2).x^{2}.y^{2}.(4x^2-y^2)`
`=(1)/(2).x^2 .y^2 .4x^2-(1)/(2).x^2 .y^2 .y^2`
`=2.x^4 .y^2-(1)/(2).x^2 .y^4`
`d.`
`((1)/(2)x-1).(2x-3)`
`=(1)/(2)x.2x-(1)/(2)x.3-2x-1.(-3)`
`=x^2-(3)/(2)x-2x+3`
`=x^2-(7)/(2)x+3`
`e.`
`(x-7).(x-5)`
`=x^2-5x-7x+35`
`=x^2-12x+35`
`f.`
`(x-1/2)(x+1/2)(4x-1)`
`=[x^2-(1/2)^2].(4x-1)`
`=(x^2-1/4).(4x-1)`
`=4x^3-x^2-x+1/4`
[Thực hiện quy tắc nhân đa thức với đa thức.]
[ `b;c;f` áp dụng HĐT `(a-b).(a+b)=a^2-b^2`]