Question

RÚT GỌN

a) \(\left(x^2+x+1\right)\left(x^2-x+1\right)\left(x^2-1\right)\)

b)\(\left(a+b+c\right)^2+\left(a-b-c\right)^2+\left(b-c-a\right)^2+\left(c-a-b\right)^2\)

Answer 1

a) \(\left(x^2+x+1\right)\left(x^2-x+1\right)\left(x^2-1\right)\)

\(=\left(x^4-x^3+x^2+x^3-x^2+x+x^2-x+1\right)\left(x^2-1\right)\)

\(=x^6-x^4+x^4-x^2+x^2-1\)

\(=x^6-1\)

b) \(\left(a+b+c\right)^2+\left(a-b-c\right)^2+\left(b-c-a\right)^2+\left(c-a-b\right)^2\)

\(=a^2+b^2+c^2+2ab+2ac+2bc+a^2+\left(-b\right)^2+\left(-c\right)^2-\\ 2ab-2ac+2bc+b^2+\left(-c\right)^2+\left(-a\right)^2-2bc-2ab+2ac\\ +c^2+\left(-a\right)^2+\left(-b\right)^2-2ac-2bc+2ab\)

\(=2a^2+2b^2+2c^2+2\cdot\left(-b\right)^2+2\cdot\left(-c\right)^2+2\cdot\left(-a\right)^2\)

\(=2a^2+2b^2+2c^2+2b^2+2c^2+2a^2\)

\(=4a^2+4b^2+4c^2\)