多项式与多项式相乘题目!(X+1)(X+2)(X+3) (X-Y)平方-(X+Y)(X-Y)(X+1)(X-2)(X-3

1.(X+1)(X+2)(X+3)
=(X+2-1)(X+2)(X+2+1)
=(X+2)([(X+2)^2-1)
=(X+2)^3-(X+2)
=X^3+6X^2+12X+4-X-2
=X^3+6X^2+11X+2
2.(X-Y)平方-(X+Y)(X-Y)
=(X-Y)^2-(X^2-Y^2)
=X^2-2XY+Y^2-X^2+Y^2
=2Y^2-2XY
3.(X+1)(X-2)(X-3)
=(X-1+2)(X-2)(X-1-2)
=(X-2)[(X-1)^2-4]
=(X-2)(X^2-2X-3)
=X^3-2X^2-3X-2X^2+4X+6
=X^3-4X^2+X+6

(X+1)(X+2)(X+3)
=(x^2+3x+2)(x+3)
=(x^3+3x^2+2x)+(3x^2+9x+6)
=x^3+6x^2+11x+6
(X-Y)平方-(X+Y)(X-Y)
=(x^2-2xy+y^2)-(x^2-y^2)
=2y^2-2xy