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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)

分类: 作业答案 • 2021-12-18 16:09:39
问题描述：

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)

答

(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

答

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+22.(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^2-2XY3.(X+1)(X-2)(X-3)=(X-1+2)(X...

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