Câu 28. Chứng minh (x + 1)(x^2 - x + 1)-(x - 1)(x^2 + x + 1) = 2 Câu 29. Chứng minh (x + y)^2 + (x - y)^2 + 2(x + y)(x - y) = 4x^2 giúp vs nha

Câu `28.` $\left(x+1\right)\left(x^2-x+1\right)-\left(x-1\right)\left(x^2+x+1\right)=2$

Ta xét VT `=` $\left(x+1\right)\left(x^2-x+1\right)-\left(x-1\right)\left(x^2+x+1\right)$

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

$=x^3+1-x^3+1$

$=x^3-x^3+1+1$

$=1+1$

$=2$ `=`  VP (đpcm)

Câu `29.`  $\left(x+y\right)^2+\left(x-y\right)^2+2\left(x+y\right)\left(x-y\right)=4x^2$

Ta xét VT `=` $\left(x+y\right)^2+\left(x-y\right)^2+2\left(x+y\right)\left(x-y\right)$

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

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

$=x^2+2xy+y^2+x^2-2xy+y^2+2x^2-$

$=x^2+x^2+2x^2+2xy-2xy+y^2+y^2-2y^2$

$=4x^2+2xy-2xy+y^2+y^2-2y^2$

$=4x^2+y^2+y^2-2y^2$

$=4x^2$ `=` VP (đpcm)