Question

初中数学题。用乘法公式进行计算。急啊~~~~~谢谢了！！

要过程的哈~
1. （2y）³-x³
2. （a+b）³-（a-b）³
3. （1+2x+x²）²
4. （x+y-z）²

Answer 1

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

Answer 2

1. （2y）³-x³
=(2y-x)(4y^2+2xy+x^2)
2. （a+b）³-（a-b）³
=2b*[(a+b)^2+(a^2-b^2)+(a-b)^2]
3. （1+2x+x²）²
=1+4x^2+x^4+2x+x^2+2x^3
4. （x+y-z）²
=x^2+y^2+z^2+2xy-2xz-2yz .

Answer 3

1. （2y）³-x³=8y³-x³
2. （a+b）³-（a-b）³=(a³+3a²b+3ab²+b³)-(a³-3a²b+3ab²-b³)=6a²b+2b³
3. （1+2x+x²）²=1+4x+x4+4x+4x³+2x²
4. （x+y-z）²

Answer 4

1. (2y-x)(4y^2+2xy+x^2)
2. 2b*[(a+b)^2+(a^2-b^2)+(a-b)^2]
3. 1+4x^2+x^4+2x+x^2+2x^3
4. x^2+y^2+z^2+2xy-2xz-2yz .