Đáp án:
a. `2x^2-38`
b. `-2x+38`
c. `4x-8`
d. `13-6x`
e. `x^3+18x^2+27`
Giải thích các bước giải:
a. `(x-1) (x+3) + (x+5)(x-7)`
`=x^2+3x-x-3+x^2-7x+5x-35`
`=2x^2-38`
b. `(x-1)( x-3)-(x+5)(x-7)`
`=x^2-3x-x+3-x^2+7x-5x+35`
`=-2x+38`
c. `(x-1)^2-(x-3)^2`
`=(x-1-x+3)(x-1+x-3)`
`=2(2x-4)`
`=4x-8`
d. `(x+2)(x-2)-(x+3)^2`
`=(x^2-4)-(x+3)^2`
`=x^2-4-x^2-6x-9`
`=13-6x`
e. `( x+3)^3-(x-3)^3+(x-3)(x^2+3x+9)`
`=x^3+9x^2+27x+27-x^3+9x^2-27x+27+x^3-27`
`=x^3+18x^2+27`