Rút gọn bt 𝐵=(𝑥 − 𝑦)^2 − 4(𝑥 − 𝑦)(𝑥 + 2𝑦) + 4(𝑥 + 2𝑦)^2.

LTKH

$B=\left(x-y\right)^2-4\left(x-y\right)\left(x+2y\right)+4\left(x+2y\right)^2$

$=x^2-2xy+y^2-4\left(x^2+xy-2y^2\right)+4\left(x^2+4xy+4y^2\right)$

$=x^2-2xy+y^2-4x^2-4xy+8y^2+4x^2+16xy+16y^2$

$=\left(x^2-4x^2+4x^2\right)+\left(y^2+8y^2+16y^2\right)+\left(-2xy-4xy+16xy\right)$

$=x^2+25y^2+10xy$

$=\left(x+5y\right)^2$.