Câu 1: Ta có: A = \(x^3+y^3+3xy=x^3+y^3+3xy\times1=x^3+y^3+3xy\left(x+y\right)\)

\(=\left(x+y\right)^3=1^3=1\)

Câu 2: Ta có: \(B=x^3-y^3-3xy=\left(x-y\right)\left(x^2+xy+y^2\right)-3xy\)

\(=x^2+xy+y^2-3xy=x^2-2xy+y^2=\left(x-y\right)^2=1^2=1\)

Câu 3: Ta có: \(C=x^3+y^3+3xy\left(x^2+y^2\right)-6x^2.y^2\left(x+y\right)\)

\(=x^3+y^3+3xy\left(x^2+2xy+y^2-2xy\right)+6x^2y^2\)

\(=x^3+y^3+3xy\left(x+y\right)^2-3xy.2xy+6x^2y^2\)

\(=x^3+y^3+3xy.1-6x^2y^2+6x^2y^3\)

\(=x^3+y^3+3xy\left(x+y\right)=\left(x+y\right)^3=1^3=1\)

Sửa đề: x+y=1

\(A=\left(x+y\right)^3-3xy\left(x+y\right)+3xy\left[\left(x+y\right)^2-2xy\right]+6x^2y^2\)

\(=1-3xy+3xy\left[1-2xy\right]+6x^2y^2\)

=1

Ta có: x^3 -3xy(x-y) -y^3 -x^2 + 2xy-y^2

= x^3 -y^3 - 3xy(x-y) -( x^2 -2xy+y^2)

= (x-y)(x^2+xy +y^2) - 3xy(x-y) -(x-y)^2

= (x-y)(x^2+xy+y^2 -3xy-x+y)

=11( x^2 -2xy+y^2 -x+y)

= 11[ (x-y)^2 -(x-y)]

= 11[ 11^2 -11]

= 11^3 -11^2=...

C1:  \(B=x^3+3xy+y^3\)

\(=\left(x+y\right)^3-3xy\left(x+y\right)+3xy\)

\(=\left(x+y\right)^3-3xy\left(x+y-1\right)\)

Thay \(x+y=1\)ta được:

\(B=1^3-3xy\left(1-1\right)=1\)

C2: \(x+y=1\)\(\Rightarrow\)\(x=1-y\)

\(B=x^3+3xy+y^3=\left(1-y\right)^3+3\left(1-y\right)y+y^3\)

\(=1-3y+3y^2-y^3+3y-3y^2+y^3=1\)

Linh_Men

a)\(M=\text{[}x^3-3xy\left(x-y\right)-y^3\text{]}-\left(x^2-2xy+y^2\right)\)

\(M=\left(x-y\right)^3-\left(x-y\right)^2\)

\(\Rightarrow M=7^3-7^2\)

\(M=294\)

b, Ta co: \(x^3+xy^2-x^2y-y^3+3\)

\(=\left(x^3-y^3\right)+\left(xy^2-x^2y\right)+3\)

\(=\left(x-y\right)^3+3xy\left(x-y\right)-xy\left(x-y\right)+3\)

= 3 ( vì x-y = 0)