Question

Khai triển đẳng thức :

a, \(\left(x+y+z\right)^2\)

b, \(\left(x+y-z\right)^2\)

c, \(\left(x-y-z\right)^2\)

Answer 1

a, (x+y+z)2

=\(x^2+y^2+z^2+2xy+2xz+2yz\)

b, (x+y−z)2

=\(x^2+y^2+z^2+2xy-2xz-2yz\)

c, (x−y−z)2

=\(x^2+y^2+z^2-2xy-2xz+2yz\)

chúc bạn học tốt ạ

Answer 2

a) Ta có: \(\left(x+y+z\right)^2=\left[\left(x+y\right)+z\right]^2\)

\(=\left(x+y\right)^2+2\left(x+y\right)z+z^2\)

\(=x^2+2xy+y^2+2xz+2yz+z^2\)

\(=x^2+y^2+z^2+2\left(xy+yz+zx\right)\)

b) Ta có: \(\left(x+y-z\right)^2=\left[\left(x+y\right)-z\right]^2\)

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

\(=x^2+2xy+y^2-2xz-2yz+z^2\)

\(=x^2+y^2+z^2+2\left(xy-yz-zx\right)\)

c) Ta có: \(\left(x-y-z\right)^2=\left[\left(x-y\right)-z\right]^2\)

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

\(=x^2-2xy+y^2-2xz-2yz+z^2\)

\(=x^2+y^2+z^2-2\left(xy+yz+zx\right)\)

Answer 3

a. \(\left(x+y+z\right)^2=[(x+y)+z]^2\)

rùi bn dựa theo hđt phân tích ra kết quả là \(x^2+y^2+z^2+2xy+2yz+2zx\)