一,计算(a+1/3)²×(a-1/3)² (读作:a加三分之一和的平方乘以a减三分之一的差的平方)(5分)就一题,30)提示:(a+b)×(a-b)=a²-b²

问题描述:

一,计算(a+1/3)²×(a-1/3)² (读作:a加三分之一和的平方乘以a减三分之一的差的平方)(5分)
就一题,30)
提示:(a+b)×(a-b)=a²-b²

(a+1/3)(a-1/3)(a+1/3)(a-1/3)
=(a² -1/9)(a²-1/9)
=(a² -1/9)²

=(A+3/1)×(A+3/1)×(A-3/1)×(A-3/1)
=(A²-9/1)(A²-9/1)
=(A-9/1)²

(a+1/3)²×(a-1/3)²
=(a²+2/3+1/9)(a²-2/3-1/9)
=a的4次方 -4/9-1/81

= {(a+1/3)*(a-1/3)}*{(a+1/3)*(a-1/3)}=(a² +1/9)*(a² +1/9)= (a² +1/9) ²

=(a+1/3)*(a-1/3)*(a+1/3)*(a-1/3)
=(a^2-1/9)^2
=a^4-2/9*(a^2)+1/81