化简
(i) 2x2(x3x)3x(x4+2x)2(x43x2)
(ii) x3y(x22x)+2xy(x3x4)
(iii) 3a2+2(a+2)3a(2a+1)
(iv) x(x+4)+3x(2x21)+4x2+4
(v) a(bc)b(ca)c(ab)
(vi) a(bc)+b(ca)+c(ab)
(vii) 4ab(ab)6a2(bb2)3b2(2a2a)+2ab(ba)
(viii) x2(x2+1)x3(x+1)x(x3x)
(ix) 2a2+3a(12a3)+a(a+1)
(x) a2(2a1)+3a+a38
(xi) 32x2(x21)+14x2(x2+x)34x(x31)
(xii) a2b(ab2)+ab2(4ab2a2)a3b(12b)
(xiii) a2b(a3a+1)ab(a42a2+2a)b(a3a21).


要做的

我们必须化简给定的表达式。

解决方案

(i) 2x2(x3x)3x(x4+2x)2(x43x2)=2x2(x3)2x2(x)3x(x4)3x(2x)2x4+6x2

=2x2+32x2+13x1+46x1+12x4+6x2

=2x52x33x56x22x4+6x2

=2x53x52x42x3+6x26x2

=x52x42x3

(ii) x3y(x22x)+2xy(x3x4)=x5y2x4y+2x4y2x5y

=x5y2x5y2x4y+2x4y

=x5y

(iii) 3a2+2(a+2)3a(2a+1)=3a2+2(a)+2(2)3a(2a)3a(1)

=3a2+2a+46a23a

=3a26a2+2a3a+4

=3a2a+4

(iv) x(x+4)+3x(2x21)+4x2+4=x2+4x+6x33x+4x2+4

=x2+4x2+4x3x+6x3+4

=5x2+x+6x3+4

(v) a(bc)b(ca)c(ab)=abacbc+abac+bc

=2ab2ac

(vi) a(bc)+b(ca)+c(ab)=abac+bcab+acbc

=abab+bcbc+acac

=0

(vii) 4ab(ab)6a2(bb2)3b2(2a2a)+2ab(ba)=4a2b4ab26a2b+6a2b26a2b2+3ab2+2ab22a2b

=4a2b6a2b2a2b4ab2+3ab2+2ab2+6a2b26a2b2

=4a2b8a2b4ab2+5ab2+0

=4a2b+ab2

(viii) x2(x2+1)x3(x+1)x(x3x)

=x4+x2x4x3x4+x2

=x4x4x4x3+x2+x2

=x4x3+2x2

(ix) 2a2+3a(12a3)+a(a+1)=2a2+3a3a(2a3)+a2+a

=2a2+3a6a1+3+a2+a

=2a2+3a6a4+a2+a

=6a4+3a2+4a

(x) a2(2a1)+3a+a38=a2(2a)a2(1)+3a+a38

=2a3a2+3a+a38

=2a3+a3a2+3a8

=3a3a2+3a8

(xi) 32x2(x21)+14x2(x2+x)34x(x31)

=32x2+232x2+14x2+2+14x2+134x1+3+34x

=32x432x2+14x4+14x334x4+34x

=32x4+14x434x4+14x332x2+34x

=6x4+x43x44+14x332x2+34x

=4x44+14x332x2+34x

=x4+14x332x2+34x

(xii) a2b(ab2)+ab2(4ab2a2)a3b(12b)

=a2+1ba2b2+1+4a1+1b2+12a2+1b2a3b+2a3b1+1

=a3ba2b3+4a2b32a3b2a3b+2a3b2

=a3ba3ba2b3+4a2b32a3b2+2a3b2

=0+3a2b3+0

=3a2b3

(xiii) a2b(a3a+1)ab(a42a2+2a)b(a3a21)

=a5ba3b+a2ba5b+2a3b2a2ba3b+a2b+b

=b

更新于: 2022 年 10 月 10 日

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