1.（2y）³-x³

题目

1.（2y）³-x³
2.（a+b）³-（a-b）³
3.（1+2x+x²）²
4.（x+y-z）²

答案

1和2：利用a³-b³=(a-b)³+3a²b-3ab²=(a-b)(a²-2ab+b²)+3ab(a-b)= (a-b)(a²+ab+b²)
1.(2y)³-x³ = (2y-x)³+ 3×4xy²- 3×2x²y = (2y-x)(4y²-4xy+x²)+3×2xy(2y-x) =(2y-x)(4y²+2xy+x²)
2.方法同上 答案：6a²b+2b³
3.(1+2x+x²)² = [(x+1)²]²= (x+1)^4
4.(x+y-z)²= x²+xy-xz+y²+xy-yz+z²-xz-yz= x²+y²+z²+2xy-2yz-2xz