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北师大版八年级下册数学书习题4.5答案

时间:2016-12-10 来源:书通网 共计4题

习题4.5第1题答案

(1)x2y2-2xy+1

=(xy)2-2•xy•1+12

=(xy-1)2

(2)9-12t+4t2

=32-2×3×2t+(2t)2

=(3-2t)2

(3)y2+y+1/4

=y2+2•y•1/2+(1/2)2

=(y+1/2)2

(4)25m2-80m+64

=(5m)2-2×5m×8+82

=(5m-8)2

(5)x2/4+xy+y2

=(x/2)2+2•x/2•y+y2

=(x/2+y)2

(6)a2b2-4ab+4

=(ab)2-2•ab•2+22

=(ab-2)2

习题4.5第2题答案

(1)(x+y)2+6(x+y)+9

=(x+y)2+2•(x+y)•3+32

=[(x+y+3)] 2

=(x+y+3)2

(2)a2-2a(b+c)+(b+c)2

=a2-2•a(b+c)+(b+c)2

=[a-(b+c)] 2

=(a-b-c)2

(3)4xy2-4x2y-y3

=-y(-4xy+4x2+y2

=-y[(2x)2-2•y+y2]

=-y(2x-y)2

(4)-a+2a2-a3

=-a(1-2a+a2

=-a(1-a)2

习题4.5第3题答案

解:满足条件的单项式可以是:2x,x2+1+2x=(x+1)2

习题4.5第4题答案

解:两个连续奇数的平方差能被8整除.设这两个连续奇数为2n-1和2n+1

则(2n+1)2-(2n-1)2

=[(2n+1)+(2n-1)][(2n+1)-(2n-1)]

=(2n+1+2n-1)(2n+1-2n+1)

=4n•2

=8n

由于n为整数,所以8n能被8整除,即(2n+1)2-(2n-1)2能被8整除

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