`4A.`
`a)A=(a+b)³+(a-b)³`
`=a³+3a²b+3ab²+b³+a³-3a²b+3ab²-b³`
`=(a³+a³)+(3a²b-3a²b)+(3ab²+3ab²)+(b³-b³)`
`=2a³+6ab²`
Áp dụng HĐT:`(A+B)³=A³+3A²B+3AB²+B³`
`(A-B)³=A³-3A²B+3AB²-B³`
`b)B=(x-y)³-3(y-x)²z+3(x-y)z²-z³`
`=(x-y)³-3.(x-y)².z+3.(x-y).z²-z³`
`=(x-y-z)³`
Áp dụng HĐT:`(A-B)³=A³-3A²B+3AB²-B³`
`4B.`
`a)C=6(c-d)(c+d)²+12(c-d)²(c+d)+(c+d)³+8(c-d)³`
`=8(c-d)³+12(c-d)²(c+d)+6(c-d)(c+d)²+(c+d)³`
`=[2(c-d)]³+3.[2(c-d)]².(c+d)+3.2(c-d).(c+d)²+(c+d)³`
`=[2(c-d)+(c+d)]³`
`=(2c-2d+c+d)³`
`=(3c-d)³`
Áp dụng HĐT:`(A-B)³=A³-3A²B+3AB²-B³`
`b)D=(m-n)³-(n+p)³-3(n+p)²(n-m)-3(n+p)(n-m)²`
`=(m-n)³-3(n+p)(n-m)²-3(n+p)²(n-m)-(n+p)³`
`=(m-n)³-3.(m-n)².(n+p)+3.(m-n).(n+p)²-(n+p)³`
`=[(m-n)-(n+p)]³`
`=(m-n-n-p)³`
`=(m-2n-p)³`
Áp dụng HĐT:`(A-B)³=A³-3A²B+3AB²-B³`
