Besides the balancing issue associated to the use of `\left`

, `\right`

, your expression can be improved introducing some modifications:

- Using
`\left( ... \right)`

for the inner expressions produces delimiters that are too big and introduce some additional horizontal space that it's superfluous in this particular case, so I think that it's better to use just `(...)`

.
- You need to use
`+{}`

so that the ending plus sign in the first line is correctly trated as an operator; analogously, you need to use `{}+`

for the first plus sign in the second line.
- Instead of using
`\left[`

, `\right.`

in the first line and `\right.`

, `\left]`

in the second line, I would suggest you to use `\bigl[`

, `\bigr]`

which don't need to be balanced in each line and produce better sized delimiters in most cases.
- The plus sign in the second line must be (according to some standard typographical rules for displayed math expressions) two-ems to the right of the alignment point.

In the following code I include, for comparison, your code (with the balancing problem solved) and then the code implementing my suggestions:

```
\documentclass[12pt]{article}
\usepackage[margin=2cm]{geometry}% just for the example
\usepackage{amsmath}
\begin{document}
\begin{equation}
\begin{split}
MSE_{II}(\overline{y}_{CST}) &= MSE_{I}(\overline{y}_{CST})
+\overline{Y}^{2}\left[ \left( c_{2}^{2}+2c_{1}c_{3} \right)V_{4,\, 0}+2c_{1}c_{2}V_{3,\,0}
+2\left(2c_{1}c_{2}+c_{3}\right)V_{3,\, 1} + \right. \\
& \left. + 2 \left(c_{1}^{2}+c_{2} \right)V_{2,\, 1}+ \left(c_{1}^{2}+2c_{2} \right)V_{2,\, 2}
+ {2c_{1}V_{1,\, 2}} \right]
\end{split}
\end{equation}
\begin{equation}
\begin{split}
MSE_{II} ( \overline{y}_{CST} ) &= MSE_{I} ( \overline{y}_{CST} )
+ \overline{Y}^{2} \bigl[ (c_{2}^{2} + 2c_{1}c_{3} ) V_{4,\, 0} + 2c_{1}c_{2} V_{3,\,0}
+ 2 ( 2c_{1}c_{2} + c_{3} ) V_{3,\, 1} +{} \\
&\qquad {}+ 2 ( c_{1}^{2} + c_{2} )V_{2,\, 1} + ( c_{1}^{2} + 2c_{2} ) V_{2,\, 2}
+ {2c_{1}V_{1,\, 2}} \bigr]
\end{split}
\end{equation}
\end{document}
```

Just reset `\rmdefault`

to the definition it had before `mathpazo`

was loaded.

```
\documentclass{article}
\let\temp\rmdefault
\usepackage{mathpazo}
\let\rmdefault\temp
\begin{document}
The quick brown fox jumps over the lazy dog.
\[
\int_a^b f(x) dx
\]
\end{document}
```

## Best Answer

there are several problems with the code used:

`array`

must be inside a math environment; this could be fixed by enclosing it in`\[ ... \]`

the alignment within the array must be specified; for this,

`\begin{array}{l}`

would work.the primes (input as apostrophes) are defined to be superscripts, so the explicit

`^`

is unwanted.the

`\left ... \right`

for the parentheses isn't needed anywhere, since everything within them is "normal" sizeextra grouping with braces isn't needed except around the multi-element subscripts

it would be equally appropriate, and perhaps simpler, to use the

`align*`

environment from`amsmath`

: