化简
(i) 2x2(x3−x)−3x(x4+2x)−2(x4−3x2)
(ii) x3y(x2−2x)+2xy(x3−x4)
(iii) 3a2+2(a+2)−3a(2a+1)
(iv) x(x+4)+3x(2x2−1)+4x2+4
(v) a(b−c)−b(c−a)−c(a−b)
(vi) a(b−c)+b(c−a)+c(a−b)
(vii) 4ab(a−b)−6a2(b−b2)−3b2(2a2−a)+2ab(b−a)
(viii) x2(x2+1)−x3(x+1)−x(x3−x)
(ix) 2a2+3a(1−2a3)+a(a+1)
(x) a2(2a−1)+3a+a3−8
(xi) 32−x2(x2−1)+14−x2(x2+x)−34x(x3−1)
(xii) a2b(a−b2)+ab2(4ab−2a2)−a3b(1−2b)
(xiii) a2b(a3−a+1)−ab(a4−2a2+2a)−b(a3−a2−1).
要做的
我们必须化简给定的表达式。
解决方案
(i) 2x2(x3−x)−3x(x4+2x)−2(x4−3x2)=2x2(x3)−2x2(x)−3x(x4)−3x(2x)−2x4+6x2
=2x2+3−2x2+1−3x1+4−6x1+1−2x4+6x2
=2x5−2x3−3x5−6x2−2x4+6x2
=2x5−3x5−2x4−2x3+6x2−6x2
=−x5−2x4−2x3
(ii) x3y(x2−2x)+2xy(x3−x4)=x5y−2x4y+2x4y−2x5y
=x5y−2x5y−2x4y+2x4y
=−x5y
(iii) 3a2+2(a+2)−3a(2a+1)=3a2+2(a)+2(2)−3a(2a)−3a(1)
=3a2+2a+4−6a2−3a
=3a2−6a2+2a−3a+4
=−3a2−a+4
(iv) x(x+4)+3x(2x2−1)+4x2+4=x2+4x+6x3−3x+4x2+4
=x2+4x2+4x−3x+6x3+4
=5x2+x+6x3+4
(v) a(b−c)−b(c−a)−c(a−b)=ab−ac−bc+ab−ac+bc
=2ab−2ac
(vi) a(b−c)+b(c−a)+c(a−b)=ab−ac+bc−ab+ac−bc
=ab−ab+bc−bc+ac−ac
=0
(vii) 4ab(a−b)−6a2(b−b2)−3b2(2a2−a)+2ab(b−a)=4a2b−4ab2−6a2b+6a2b2−6a2b2+3ab2+2ab2−2a2b
=4a2b−6a2b−2a2b−4ab2+3ab2+2ab2+6a2b2−6a2b2
=4a2b−8a2b−4ab2+5ab2+0
=−4a2b+ab2
(viii) x2(x2+1)−x3(x+1)−x(x3−x)
=x4+x2−x4−x3−x4+x2
=x4−x4−x4−x3+x2+x2
=−x4−x3+2x2
(ix) 2a2+3a(1−2a3)+a(a+1)=2a2+3a−3a(2a3)+a2+a
=2a2+3a−6a1+3+a2+a
=2a2+3a−6a4+a2+a
=−6a4+3a2+4a
(x) a2(2a−1)+3a+a3−8=a2(2a)−a2(1)+3a+a3−8
=2a3−a2+3a+a3−8
=2a3+a3−a2+3a−8
=3a3−a2+3a−8
(xi) 32x2(x2−1)+14x2(x2+x)−34x(x3−1)
=32x2+2−32x2+14x2+2+14x2+1−34x1+3+34x
=32x4−32x2+14x4+14x3−34x4+34x
=32x4+14x4−34x4+14x3−32x2+34x
=6x4+x4−3x44+14x3−32x2+34x
=4x44+14x3−32x2+34x
=x4+14x3−32x2+34x
(xii) a2b(a−b2)+ab2(4ab−2a2)−a3b(1−2b)
=a2+1b−a2b2+1+4a1+1b2+1−2a2+1b2−a3b+2a3b1+1
=a3b−a2b3+4a2b3−2a3b2−a3b+2a3b2
=a3b−a3b−a2b3+4a2b3−2a3b2+2a3b2
=0+3a2b3+0
=3a2b3
(xiii) a2b(a3−a+1)−ab(a4−2a2+2a)−b(a3−a2−1)
=a5b−a3b+a2b−a5b+2a3b−2a2b−a3b+a2b+b
=b