Question

ai giúp em vs huhu

bai 1 : chứng minh

\(a,\left(a-b\right)^3=-\left(b-a\right)^3\)

\(b,\left(a-b\right)^2=\left(a+b^{ }2\right)\)

c, \(\left(x+y\right)^3=x\left(x-3y^{ }\right)^2+y\left(y-3x\right)^2\)

d\(\left(x+y^{ }\right)^3-\left(x-y^{ }\right)^3=2y\left(y^2+3x^2\right)\)

Answer 1

a) \(\left(a-b\right)^3=-\left(b-a\right)^3\)

Ta có: \(\left(a-b\right)^3=a^3-3a^2b+3ab^2-b^3\)

\(=-\left(b^3-3ab^2+3a^2b-a^3\right)\)

\(=-\left(b-a\right)^3\)

Vậy..

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

Ta có: \(x\left(x-3y\right)^2+y\left(y-3x\right)^2\)

\(=x^3-6x^2y+9xy^2+y^3+y^3-6xy^2+9x^2y\)

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

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

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

Vậy..

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

Ta có: \(\left(x+y\right)^3-\left(x-y\right)^3\)

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

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

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

Vậy...

Answer 2

b đề bị gi` thế