Question

Answer 1

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

b) \(m^3+n^3+p^3-3nmp=\left(m^3+3m^2n+3mn^2+n^3\right)+p^3-3mnp-3m^2n-3mn^2=\left(m+n\right)^3+p^3-3mn\left(m+n+p\right)=\left(m+n+p\right)\left[\left(m+n\right)^2-\left(m+n\right)p+p^2\right]-3mn\left(m+n+p\right)=\left(m+n+p\right)\left(m^2+2mn+n^2-mp-np+p^2-3mn\right)=\left(m+n+p\right)\left(m^2+n^2+p^2-mn-np-mp\right)\left(đpcm\right)\)