Question

x^2+(x+2)(x+10)-2 (2)设n是自然数,求证（n+5)^2-(n-3)^2能被16整除

Answer 1

(1)x²+(x+2)(x+10)-2

=x²+x²+12x+20-2

=2x²+12x+18

=2(x²+6x+9)

=2(x+3)²

(2)、证明：

(n+5)²-(n-3)²

=[(n+5)+(n-3)][(n+5)-(n-3)]

=(n+5+n-3)(n+5-n+3)

=(2n+2)*8

=16(n+1)

∵n是自然数

∴16(n+1)能被16整除

∴(n+5)²-(n-3)²能被16整除