Question

gấp ạ

Answer 1

a.

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

b.

\(m^3+n^3+p^3-3mnp=m^3+n^3+3mn\left(m+n\right)-3mn\left(m+n\right)+p^3-3mnp\)

\(=\left(m+n\right)^3+p^3-3mn\left(m+n+p\right)\)

\(=\left(m+n+p\right)\left[\left(m+n\right)^2-\left(m+n\right)p+p^2\right]-3mn\left(m+n+p\right)\)

\(=\left(m+n+p\right)\left(m^2+n^2+p^2+2mn-mp-np\right)-3mn\left(m+n+p\right)\)

\(=\left(m+n+p\right)\left(m^2+n^2+p^2-mn-np-mp\right)\)