State True or False:

The expression $abc+a{b}^{2}c+a^{2}bc$ has to be added to the expression $\left(a^2{b}^2{c}^2+a{b}^{2}c+a^{2}bc+abc\right)$ to obtain $\left(a^2{b}^2{c}^2+2abc\right)$.

$abc+a{b}^{2}c+a^{2}bc+\left(a^2{b}^2{c}^2+a{b}^{2}c+a^{2}bc+abc\right)$

Collecting the like terms together, we get

$=a^2{b}^2{c}^2+(a{b}^{2}c+a{b}^{2}c)+(a^{2}bc+a^{2}bc)+(abc+abc)$

$=a^2{b}^2{c}^2+2a{b}^{2}c+2a^{2}bc+2abc$

Since, $a^2{b}^2{c}^2+2a{b}^{2}c+2a^{2}bc+2abc\ne \left(a^2{b}^2{c}^2+2abc\right)$

Therefore, the given statement is False.